Foreword 1. Introduction 2. Interactions at the grain level 3. The granular solid: statics and elasticity 4. The granular solid: plasticity 5. Granular gases 6. The granular liquid 7. Immersed granular media 8. Erosion and sediment transport 9. Geomorphology References Index.

Granular Media: Between Fluid and Solid

The 'plug' flow emerging from a long rotating tube into a large stationary reservoir has been used in an experimental investigation of centrifugally unstable swirling jets. A moderate Reynolds number, Re = 1000, was studied extensively, and swirl numbers, S, the ratio of nozzle exit rotating speed to the mean mass axial velocity, were in the range 0-1.1. Four regimes were covered: non-swirling jets with S=0, weakly swirling jets in the range 0 S c2 , where S c1 =0.6 and S c2 = 0.88. Particular attention was paid to the dominant role of the underlying vortical flow structures and their dynamic evolution. Kelvin-Helmholtz (K-H) instability in the axial shear layer, generated by the axial velocity, leading to vortex ring formation, dominated non-swirling and weakly swirling jets

An experimental investigation of swirling jets

An erodible bed sheared by a fluid flow, gas or liquid, is generally unstable, and bed forms grow. This review discusses the following issues, in light of the recent literature: What are the relevant dynamical mechanisms controlling the emergence of bed forms? Do they form by linear instability or nonlinear processes such as pattern coarsening? What determines their timescales and length scales, so different in air and water? What are the similarities and differences between aeolian and subaqueous patterns? What is the influence of the mode of transport: bed load, saltation, or suspension? Can bed forms emerge under any hydrodynamical regime, laminar and turbulent? Guided by these questions, we propose a unified description of bed-form growth and saturation, emphasizing the hydrodynamical regime in the inner layer and the relaxation phenomena associated with particle transport.

Sand Ripples and Dunes

A theoretical model based on a depth-averaged version of two-phase flow equations is developed to describe the initiation of underwater granular avalanches. The rheology of the granular phase is based on a shear-rate-dependent critical state theory, which combines a critical state theory proposed by Roux & Radjai (1998), and a rheological model recently proposed for immersed granular flows. Using those phenomenological constitutive equations, the model is able to describe both the dilatancy effects experienced by the granular skeleton during the initial deformations and the rheology of wet granular media when the flow is fully developed. Numerical solutions of the two-phase flow model are computed in the case of a uniform layer of granular material fully immersed in a liquid and suddenly inclined from horizontal. The predictions are quantitatively compared with experiments by Pailha, Nicolas & Pouliquen (2008), who have studied the role of the initial volume fraction on the dynamics of underwater granular avalanches. Once the rheology is calibrated using steady-state regimes, the model correctly predicts the complex transient dynamics observed in the experiments and the crucial role of the initial volume fraction. Quantitative predictions are obtained for the triggering time of the avalanche, for the acceleration of the layer and for the pore pressure.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112009007460

A two-phase flow description of the initiation of underwater granular avalanches

The stability of a granular bed sheared by a liquid flow is investigated using an erosion-deposition model for the moving grains. Extending to arbitrary wave number a previous long wave analysis [F. Charru and E. J. Hinch, J. Fluid Mech. 550, 111 (2006)], this study shows that short waves are stabilized by a crest-erosion mechanism that is absent when the local particle flux is assumed to be in equilibrium with the local bed shear stress. The cutoff length associated with this mechanism scales on a deposition length of the particles. This characteristic length is similar, although of a different physical nature, to the inertial length involved in relaxation models of dune dynamics under the wind. Two stabilizing mechanisms cooperate for the most amplified wave number: the new crest-erosion mechanism and the gravity force parallel to the local slope of the inclined bed. The predictions of this model are compared to observations, showing better agreement than previous stability analyses, which strongly unde...

Selection of the ripple length on a granular bed sheared by a liquid flow

The transport inception of immersed grains is studied experimentally with laminar flow conditions in a Hele-Shaw cell when varying the tilt angle of the cell and the water flow rate. Varying these two parameters, grains are either motionless, rolling on the bed surface, or avalanching downwards. This paper focuses on the determination of the onset for grain motion either by erosion or by avalanche. For a horizontal interface, onset for erosion corresponds to a constant critical Shields number θc=0.14 at small particle Reynolds number (Red 1). For tilted bed, the onset of erosion increases when the flow is opposed to gravity. Both results are compared to a standard model based on a balance of the forces acting on a single grain lying on a tilted plane. When tilt angles are large, avalanches occur. The maximum angle of stability is modified by the flow and increases slightly when the flow acts against gravity. This behavior is compared to a c...

Onset of erosion and avalanche for an inclined granular bed sheared by a continuous laminar flow

The absolute (AI)/convective (CI) nature of the instability is determined in the family of swirling jet/wake shear layers considered by Martin and Meiburg [Phys. Fluids 6, 424 (1994)] and Lim and Redekopp [Eur. J. Mech. B/Fluids 17, 165 (1998)]. This idealized model includes as essential ingredients both the centrifugal instability associated with the swirl difference and the Kelvin–Helmholtz instability associated with the swirl and axial velocity differences between the core and the outer flow. Centrifugally stabilizing or destabilizing swirl differences are found to promote AI, but a centrifugally destabilizing configuration is more effective in triggering such a transition. For sufficiently large swirl differences, both co-flowing jets and wakes may become AI. In the case of jets, a centrifugally destabilizing swirl difference first brings about AI via the axisymmetric mode m=0 in a large range of mean swirl values. By contrast, a centrifugally stabilizing swirl difference triggers AI via the helical mode m=−∞. In the case of wakes, a centrifugally destabilizing swirl difference leads to AI via the bending mode m=1 whereas a centrifugally stabilizing swirl difference triggers AI via various negative helical modes m=−1,−2, etc.

/pdf/absolute-and-convective-instabilities-of-a-swirling-jet-wake-45rbr5jbn5.pdf

Absolute and convective instabilities of a swirling jet/wake shear layer

We study water-immersed granular avalanches in a long rectangular cell of small thickness. By video means, both the angle of the granular pile and the velocity profiles of the grains across the depth are recorded as a function of time. These measurements give access to the instantaneous granular flux. By inclining the pile at initial angles larger than the maximum angle of stability, avalanches are triggered and last for a long time, up to several hours for small grains, during which both the slope angle and the granular flux relax slowly. We show that the relaxation is quasi-steady so that there is no inertia: the relaxation at a given time is controlled only by the slope angle at that time. This allows us to adapt a frictional model developed recently for dry or water-immersed grains flowing in stationary conditions. This model succeeds well in reproducing our unsteady avalanche flows, namely the flowing layer thickness, the granular flux and the temporal relaxation of the slope. When a water counter-flow is applied along the pile, the granular avalanches are slowed down and behave as if granular friction were increased by an amount proportional to the water flow. All these findings are also reproduced well with the same friction model by taking into account the additional fluid force.

/pdf/relaxation-dynamics-of-water-immersed-granular-avalanches-4u9vn22ff2.pdf

Thomas Loiseleux

Papers

Onset of erosion and avalanche for an inclined granular bed sheared by a continuous laminar flow

Absolute and convective instabilities of a swirling jet/wake shear layer

Relaxation dynamics of water-immersed granular avalanches

Dynamique d'avalanches sous-marines en cellule de Hele-Shaw