The kinematics of bidisperse granular roll waves

Viroulet, Sylvain; Baker, James; Rocha, Francisco M.; Johnson, Chris; Kokelaar, B. P.; Gray, J.O.

doi:10.1017/jfm.2018.348

Cited by 35 publications

(37 citation statements)

References 61 publications

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“…Interestingly, simulations with ξ = 1 show the tendencies to produce wave-like instabilities in situations without entrainment. This behaviour can be explained by the rheological model and is commonly observed [50]. We find that the classic Voellmy model does not tend to produce these instabilities.…”

Section: A)supporting

confidence: 68%

Constraints on Entrainment and Deposition Models in Avalanche Simulations from High-Resolution Radar Data

Rauter

Köhler

2019

Geosciences

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Depth-integrated simulations of snow avalanches have become a central part of risk analysis and mitigation. However, the common practice of applying different model parameters to mimic different avalanches is unsatisfying. In here, we analyse this issue in terms of two differently sized avalanches from the full-scale avalanche test-site Vallée de la Sionne, Switzerland. We perform depth-integrated simulations with the toolkit OpenFOAM, simulating both events with the same set of model parameters. Simulation results are validated with high-resolution position data from the GEODAR radar. Rather than conducting extensive post-processing to match radar data to the output of the simulations, we generate synthetic flow signatures inside the flow model. The synthetic radar data can be directly compared with the GEODAR measurements. The comparison reveals weaknesses of the model, generally at the tail and specifically by overestimating the runout of the smaller event. Both issues are addressed by explicitly considering deposition processes in the depth-integrated model. The new deposition model significantly improves the simulation of the small avalanche, making it starve in the steep middle part of the slope. Furthermore, the deposition model enables more accurate simulations of deposition patterns and volumes and the simulation of avalanche series that are influenced by previous deposits.

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Section: A)supporting

confidence: 68%

Constraints on Entrainment and Deposition Models in Avalanche Simulations from High-Resolution Radar Data

Rauter

Köhler

2019

Geosciences

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“…Numerical solutions are calculated using a high-resolution semi-discrete nonoscillatory central (NOC) scheme for convection-diffusion equations (Kurganov & Tadmor 2000). This method has proved its ability to solve similar systems of conservation laws for erosion-deposition waves (Edwards & Gray 2015;Edwards et al 2017), segregation-induced finger formation (Baker et al 2016b) and bi-disperse roll waves (Viroulet et al 2018). The equations are solved in conservative form, where U = (h, hū, hv) T is the vector of conserved fields, with U x and U y being the derivatives of U with respect to x and y, respectively.…”

Section: Methodsmentioning

confidence: 99%

Self-channelisation and levee formation in monodisperse granular flows

2019

Self Cite

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Dense granular flows can spontaneously self-channelise by forming a pair of parallel-sided static levees on either side of a central flowing channel. This process prevents lateral spreading and maintains the flow thickness, and hence mobility, enabling the grains to run out considerably further than a spreading flow on shallow slopes. Since levees commonly form in hazardous geophysical mass flows, such as snow avalanches, debris flows, lahars and pyroclastic flows, this has important implications for risk management in mountainous and volcanic regions. In this paper an avalanche model that incorporates frictional hysteresis, as well as depth-averaged viscous terms derived from the $\unicode[STIX]{x1D707}(I)$-rheology, is used to quantitatively model self-channelisation and levee formation. The viscous terms are crucial for determining a smoothly varying steady-state velocity profile across the flowing channel, which has the important property that it does not exert any shear stresses at the levee–channel interfaces. For a fixed mass flux, the resulting boundary value problem for the velocity profile also uniquely determines the width and height of the channel, and the predictions are in very good agreement with existing experimental data for both spherical and angular particles. It is also shown that in the absence of viscous (second-order gradient) terms, the problem degenerates, to produce plug flow in the channel with two frictionless contact discontinuities at the levee–channel margins. Such solutions are not observed in experiments. Moreover, the steady-state inviscid problem lacks a thickness or width selection mechanism and consequently there is no unique solution. The viscous theory is therefore a significant step forward. Fully time-dependent numerical simulations to the viscous model are able to quantitatively capture the process in which the flow self-channelises and show how the levees are initially emplaced behind the flow head. Both experiments and numerical simulations show that the height and width of the channel are not necessarily fixed by these initial values, but respond to changes in the supplied mass flux, allowing narrowing and widening of the channel long after the initial front has passed by. In addition, below a critical mass flux the steady-state solutions become unstable and time-dependent numerical simulations are able to capture the transition to periodic erosion–deposition waves observed in experiments.

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“…It is important to note that the depth-averaged viscous terms (Gray & Edwards 2014;Baker, Barker & Gray 2016a), which are crucial for the formation of leveed channels on non-erodible slopes (Rocha, Johnson & Gray 2019), can be neglected here because the retrogressive failures are planar. It is, however, anticipated that viscous terms could well be important for non-planar retrogressive waves, where cross-slope gradients in the velocity will develop naturally, or, for the correct cutoff frequency and coarsening dynamics of roll waves and erosion-deposition waves that may form downstream of the failure front (Gray & Edwards 2014;Edwards & Gray 2015;Viroulet et al 2018). Gray & Edwards (2014) showed that, to leading order in the aspect ratio, both the inviscid avalanche equations (3.1)-(3.2) and the dynamic friction law of Pouliquen & Forterre (2002) emerge naturally from depth averaging the µ(I)-rheology for granular flows (GDR-MiDi 2004;Jop et al 2006).…”

Section: Governing Equationsmentioning

confidence: 99%

Retrogressive failure of a static granular layer on an inclined plane

et al. 2019

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When a layer of static grains on a sufficiently steep slope is disturbed, an upslope-propagating erosion wave, or retrogressive failure, may form that separates the initially static material from a downslope region of flowing grains. This paper shows that a relatively simple depth-averaged avalanche model with frictional hysteresis is sufficient to capture a planar retrogressive failure that is independent of the cross-slope coordinate. The hysteresis is modelled with a non-monotonic effective basal friction law that has static, intermediate (velocity decreasing) and dynamic (velocity increasing) regimes. Both experiments and time-dependent numerical simulations show that steadily travelling retrogressive waves rapidly form in this system and a travelling wave ansatz is therefore used to derive a one-dimensional depth-averaged exact solution. The speed of the wave is determined by a critical point in the ordinary differential equation for the thickness. The critical point lies in the intermediate frictional regime, at the point where the friction exactly balances the downslope component of gravity. The retrogressive wave is therefore a sensitive test of the functional form of the friction law in this regime, where steady uniform flows are unstable and so cannot be used to determine the friction law directly. Upper and lower bounds for the existence of retrogressive waves in terms of the initial layer depth and the slope inclination are found and shown to be in good agreement with the experimentally determined phase diagram. For the friction law proposed by Edwardset al.(J. Fluid. Mech., vol. 823, 2017, pp. 278–315,J. Fluid. Mech., 2019, (submitted)) the magnitude of the wave speed is slightly under-predicted, but, for a given initial layer thickness, the exact solution accurately predicts an increase in the wave speed with higher inclinations. The model also captures the finite wave speed at the onset of retrogressive failure observed in experiments.

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The kinematics of bidisperse granular roll waves

Cited by 35 publications

References 61 publications

Constraints on Entrainment and Deposition Models in Avalanche Simulations from High-Resolution Radar Data

Constraints on Entrainment and Deposition Models in Avalanche Simulations from High-Resolution Radar Data

Self-channelisation and levee formation in monodisperse granular flows

Retrogressive failure of a static granular layer on an inclined plane

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