Shallow granular flows

Takagi, Daisuke; McElwaine, J. N.; Huppert, Herbert E.

doi:10.1103/physreve.83.031306

Cited by 24 publications

(106 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although this approximation is crude, in that it does not explicitly resolve the basal entrainment or deposition, Edwards & Gray (2015) showed that it was able to predict accurately the amplitude, wavelength and coarsening dynamics of erosion-deposition waves that spontaneously form in a long channel from a continuous inflow. They observed that typical waves had a ratio of peak height to static layer depth of 2.6 and a typical mobile wavelength of 59 cm, which are both very similar to the waves observed by Takagi, McElwaine & Huppert (2011) in their low-inflow-rate experiments.…”

Section: Introductionsupporting

confidence: 66%

Formation of levees, troughs and elevated channels by avalanches on erodible slopes

et al. 2017

View full text Add to dashboard Cite

Snow avalanches are typically initiated on marginally stable slopes with a surface layer of fresh snow that may easily be incorporated into them. The erosion of snow at the front is fundamental to the dynamics and growth of snow avalanches and they may rapidly bulk up, making them much more destructive than the initial release. Snow may also deposit at the rear, base and sides of the flow and the net balance of erosion and deposition determines whether an avalanche grows or decays. In this paper, small-scale analogue experiments are performed on a rough inclined plane with a static erodible layer of carborundum grains. The static layer is prepared by slowly closing down a flow from a hopper at the top of the slope. This leaves behind a uniform-depth layer of thickness $h_{stop}$ at a given slope inclination. Due to the hysteresis of the rough bed friction law, this layer can then be inclined to higher angles provided that the thickness does not exceed $h_{start}$, which is the maximum depth that can be held static on a rough bed. An avalanche is then initiated on top of the static layer by releasing a fixed volume of carborundum grains. Dependent on the slope inclination and the depth of the static layer three different behaviours are observed. For initial deposit depths above $h_{stop}$, the avalanche rapidly grows in size by progressively entraining more and more grains at the front and sides, and depositing relatively few particles at the base and tail. This leaves behind a trough eroded to a depth below the initial deposit surface and whose maximal areal extent has a triangular shape. Conversely, a release on a shallower slope, with a deposit of thickness $h_{stop}$, leads to net deposition. This time the avalanche leaves behind a levee-flanked channel, the floor of which lies above the level of the initial deposit and narrows downstream. It is also possible to generate avalanches that have a perfect balance between net erosion and deposition. These avalanches propagate perfectly steadily downslope, leaving a constant-width trail with levees flanking a shallow trough cut slightly lower than the initial deposit surface. The cross-section of the trail therefore represents an exact redistribution of the mass reworked from the initial static layer. Granular flow problems involving erosion and deposition are notoriously difficult, because there is no accepted method of modelling the phase transition between static and moving particles. Remarkably, it is shown in this paper that by combining Pouliquen & Forterre’s (J. Fluid Mech., vol. 453, 2002, pp. 133–151) extended friction law with the depth-averaged $\unicode[STIX]{x1D707}(I)$-rheology of Gray & Edwards (J. Fluid Mech., vol. 755, 2014, pp. 503–544) it is possible to develop a two-dimensional shallow-water-like avalanche model that qualitatively captures all of the experimentally observed behaviour. Furthermore, the computed wavespeed, wave peak height and stationary layer thickness, as well as the distance travelled by decaying avalanches, are all in good quantitative agreement with the experiments. This model is therefore likely to have important practical implications for modelling the initiation, growth and decay of snow avalanches for hazard assessment and risk mitigation.

show abstract

Section: Introductionsupporting

confidence: 66%

Formation of levees, troughs and elevated channels by avalanches on erodible slopes

et al. 2017

View full text Add to dashboard Cite

show abstract

“…All the results in this paper were performed on a slope of 32 • to the horizontal which is just above the minimum angle for steady flow. At higher angles steady flows were hard to achieve because roll waves develop while at lower angles discrete avalanches occur at lower mass flow rates [3]. The flows in the experiments could be maintained indefinitely by transferring the grains that flowed off The thickness and surface velocity of the flows were measured 2 m down the slope where the flows were steady and no longer depended on the x position.…”

Section: Laboratory Experimentsmentioning

confidence: 99%

“…When a granular material is released steadily from a localised source down a rough plane inclined at a range of angles, a steady flow develops between static levées down the slope [1][2][3]. Remarkably, however, the surface of the flowing region is not parallel to the inclined plane, but is curved across the slope with the height decreasing from the middle toward the levées.…”

Section: Introductionmentioning

confidence: 95%

“…We carried out a series of laboratory experiments to investigate the flow of granular material from a localised source on a rough inclined plane (described in more detail in [3]). The experimental set up is shown in Fig.…”

Section: Laboratory Experimentsmentioning

confidence: 99%

“…A mathematical model is developed and applied to the experiments previously presented in detail in [3], which can be regarded as a granular channel flow. The model is consistent with the experimental observation that the height of the steady flow decreases from the middle of the flow particularly toward the margins, where the downslope velocity varies considerably in the cross-slope direction.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Surface curvature of steady granular flows

2012

Self Cite

View full text Add to dashboard Cite

Laboratory experiments have shown that the steady flow of granular material down a rough inclined plane has a surface that is not parallel to the plane, but has a curvature across the slope with the height increasing toward the middle of the flow. We study this observation by postulating a new granular rheology, similar to that of a second order fluid. This model is applied to the experiments using a shallow water approximation, given that the depth of the flow is much smaller than the width. The model predicts that a second normal stress difference allows cross-slope height variations to develop in regions with considerable cross-slope velocity shear, consistent with the experiments. The model also predicts the development of lateral eddies, which are yet to be observed.

show abstract

Acoustic signals generated in inclined granular flows

et al. 2015

View full text Add to dashboard Cite

Spontaneous avalanching in specific deserts produces a low‐frequency sound known as “booming.” This creates a puzzle, because avalanches down the face of a dune result in collisions between sand grains that occur at much higher frequencies. Reproducing this phenomenon in the laboratory permits a better understanding of the underlying mechanisms for the generation of such lower frequency acoustic emissions, which may also be relevant to other dry granular flows. Here we report measurements of low‐frequency acoustical signals, produced by dried “sounding” sand (sand capable of booming in the desert) flowing down an inclined chute. The amplitude of the signal diminishes over time but reappears upon drying of the sand. We show that the presence of this sound in the experiments may provide supporting evidence for a previously published “waveguide” explanation for booming. Also, we propose a model based on kinetic theory for a sheared inclined flow in which the flowing layer exhibits “breathing” modes superimposed on steady shearing. The predicted oscillation frequency is of a similar order of magnitude as the measurements, indicating that small perturbations can sustain oscillations of a low frequency. However, the frequency is underestimated, which indicates that the stiffness has been underestimated. Also, the model predicts a discrete spectrum of frequencies, instead of the broadband spectrum measured experimentally.

show abstract

Shallow granular flows

Cited by 24 publications

References 38 publications

Formation of levees, troughs and elevated channels by avalanches on erodible slopes

Formation of levees, troughs and elevated channels by avalanches on erodible slopes

Surface curvature of steady granular flows

Acoustic signals generated in inclined granular flows

Contact Info

Product

Resources

About