Flow rule, self-channelization and levees in unconfined granular flows

Unconfined granular flows along an inclined plane are investigated experimentally. During a long transient, the flow gets confined by quasistatic banks but still spreads laterally towards a well-defined asymptotic state following a nontrivial process. Far enough from the banks a scaling for the depth averaged velocity is obtained, which extends the one obtained for homogeneous steady flows. Close to jamming it exhibits a crossover towards a nonlocal rheology. We show that the levees, commonly observed along the sides of the deposit upon interruption of the flow, disappear for long flow durations. We demonstrate that the morphology of the deposit builds up during the flow, in the form of an underlying static layer, which can be deduced from surface velocity profiles, by imposing the same flow rule everywhere in the flow.Comment: 4 pages, 5 figure

Numerical Modeling of Iceberg Capsizing Responsible for Glacial Earthquakes

The capsizing of icebergs calved from marine‐terminating glaciers generate horizontal forces on the glacier front, producing long‐period seismic signals referred to as glacial earthquakes. These forces can be estimated by broadband seismic inversion, but their interpretation in terms of magnitude and waveform variability is not straightforward. We present a numerical model for fluid drag that can be used to study buoyancy‐driven iceberg capsize dynamics and the generated contact forces on a calving face using the finite‐element approach. We investigate the sensitivity of the force to drag effects, iceberg geometry, calving style, and initial buoyancy. We show that there is no simple relationship between force amplitude and iceberg volume, and similar force magnitudes can be reached for different iceberg sizes. The force history and spectral content varies with the iceberg attributes. The iceberg aspect ratio primarily controls the capsize dynamics, the force shape, and force frequency, whereas the iceberg height has a stronger impact on the force magnitude. Iceberg hydrostatic imbalance generates contact forces with specific frequency peaks that explain the variability in glacial earthquake dominant frequency. For similar icebergs, top‐out and bottom‐out events have significantly different capsize dynamics leading to larger top‐out forces especially for thin icebergs. For realistic iceberg dimensions, we find contact‐force magnitudes that range between 5.6 × 1011 and 2 × 1014 kg·m, consistent with seismic observations. This study provides a useful framework for interpreting glacial earthquake sources and estimating the ice mass loss from coupled analysis of seismic signals and modeling results

Complex force history of a calving-generated glacial earthquake derived from broadband seismic inversion

The force applied to the Earth by the calving of two icebergs at Jakobshavn Isbrae, Greenland, has been quantified. The source force history was recovered by inversion of regional broadband seismograms without any a priori constraint on the source time function, in contrast with previous studies. For periods 10-100 s, the three-component force can be obtained from distant stations alone and is proportional to the closest station seismograms. This inversion makes it possible to quantify changes of the source force direction and amplitude as a function of time and frequency. A detailed comparison with a video of the event was used to identify four forces associated with collision, then bottom-out and top-out rotation of the first and second icebergs, and ice mélange motion. Only the two iceberg rotations were identified in previous studies. All four processes are found here to contribute to the force amplitude and variability. Such a complete time-frequency force history provides unique dynamical constraints for mechanical calving models.ERC. Grant Number: ERC-CG-2013-PE10-617472 ANR. Grant Number: ANR-11-BS01-0016 LANDQUAKES, CNCS‐UEFISCDI. Grant Number: PN-II-ID-PCE-2011-3-004

Modelling capsizing icebergs in the open ocean

At near-grounded glacier termini, calving can lead to the capsize of kilometre-scale (i.e. gigatons) unstable icebergs. The transient contact force applied by the capsizing iceberg on the glacier front generates seismic waves that propagate over teleseismic distances. The inversion of this seismic signal is of great interest to get insight into actual and past capsize dynamics. However, the iceberg size, which is of interest for geophysical and climatic studies, cannot be recovered from the seismic amplitude alone. This is because the capsize is a complex process involving interactions between the iceberg, the glacier and the surrounding water. This paper presents a first step towards the construction of a complete model, and is focused on the capsize in the open ocean without glacier front nor ice-mélange. The capsize dynamics of an iceberg in the open ocean is captured by computational fluid dynamics (CFD) simulations, which allows assessing the complexity of the fluid motion around a capsizing iceberg and how far the ocean is affected by iceberg rotation. Expressing the results in terms of appropriate dimensionless variables, we show that laboratory scale and field scale capsizes can be directly compared. The capsize dynamics is found to be highly sensitive to the iceberg aspect ratio and to the water and ice densities. However, dealing at the same time with the fluid dynamics and the contact between the iceberg and the deformable glacier front requires highly complex coupling that often goes beyond actual capabilities of fluid-structure interaction softwares. Therefore, we developed a semi-analytical simplified fluid-structure model (SAFIM) that can be implemented in solid mechanics computations dealing with contact dynamics of deformable solids. This model accounts for hydrodynamic forces through calibrated drag and added-mass effects, and is calibrated against the reference CFD simulations. We show that SAFIM significantly improves the accuracy of the iceberg motion compared with existing simplified models. Various types of drag forces are discussed. The one that provides the best results is an integrated pressure-drag proportional to the square of the normal local velocity at the iceberg’s surface, with the drag coefficient depending linearly on the iceberg’s aspect ratio. A new formulation based on simplified added-masses or computed added-mass proposed in the literature, is also discussed. We study in particular the change of hydrodynamic-induced forces and moments acting on the capsizing iceberg. The error of the simulated horizontal force ranges between 5 and 25 per cent for different aspect ratios. The added-masses affect the initiation period of the capsize, the duration of the whole capsize being better simulated when added-masses are accounted for. The drag force mainly affects the amplitude of the fluid forces and this amplitude is best predicted without added-masses.he authors acknowledge funding from ANR (contract ANR-11- BS01-0016 LANDQUAKES), ERC (contract ERC-CG-2013-PE10-617472 SLIDEQUAKES), DGA-MRIS and IPGP - Univer-sit´e de Paris ED560 (STEP’UP), which has made this work possible. The authors acknowledge Justin Burton for providing us with the data from laboratory experiments. The authors are also very grateful to Franc¸ois Charru, Emmanuel de Langre and Evgeniy A. Podolskiy for fruitful discussions, and the reviewers (Jason M. Amundson and Bradley P. Lipovsky) for helpful comments

A "well-balanced" finite volume scheme for blood flow simulation

We are interested in simulating blood flow in arteries with a one dimensional model. Thanks to recent developments in the analysis of hyperbolic system of conservation laws (in the Saint-Venant/ shallow water equations context) we will perform a simple finite volume scheme. We focus on conservation properties of this scheme which were not previously considered. To emphasize the necessity of this scheme, we present how a too simple numerical scheme may induce spurious flows when the basic static shape of the radius changes. On contrary, the proposed scheme is "well-balanced": it preserves equilibria of Q = 0. Then examples of analytical or linearized solutions with and without viscous damping are presented to validate the calculations. The influence of abrupt change of basic radius is emphasized in the case of an aneurism.Comment: 36 page

Monitoring Greenland ice sheet buoyancy-driven calving discharge using glacial earthquakes

Since the 2000s, Greenland ice sheet mass loss has been accelerating, followed by increasing numbers of glacial earthquakes (GEs) at near-grounded glaciers. GEs are caused by calving of km-scale icebergs which capsize against the terminus. Seismic record inversion allows a reconstruction of the history of GE sources which captures capsize dynamics through iceberg-to-terminus contact. When compared with a catalog of contact forces from an iceberg capsize model, seismic force history accurately computes calving volumes while the earthquake magnitude fails to uniquely characterize iceberg size, giving errors up to 1 km ³ . Calving determined from GEs recorded ateight glaciers in 1993–2013 accounts for up to 21% of the associated discharge and 6% of the Greenland mass loss. The proportion of discharge attributed to capsizing calving may be underestimated by at least 10% as numerous events could not be identified by standard seismic detections (Olsen and Nettles, 2018). While calving production tends to stabilize in East Greenland, Western glaciers have released more and larger icebergs since 2010 and have become major contributors to Greenland dynamic discharge. Production of GEs and calving behavior are controlled by glacier geometry with bigger icebergs being produced when the terminus advances in deepening water. We illustrate how GEs can help in partitioning and monitoring Greenland mass loss and characterizing capsize dynamics

The influence of localised size reorganisation on short-duration bidispersed granular flows

We investigate experimentally the runout resulting from the collapse of a granular column containing two particle species that differ in size only. The experimental configuration is strictly twodimensional (only one particle per width of the experimental tank) and we explore both the role of the initial arrangement and proportion of the two particle sizes in the column, using high-speed videography, and by determining the centres of mass of the big and small particles in the initial column and the final deposit. The duration of the experiment is sufficiently short that large-scale segregation does not occur, however, we find a clear dependence of runout on both initial mixture arrangement and proportion for all conditions. We investigated this observation through detailed analysis of the flow front motion, and identify a characteristic "stopping" phase when dissipation dominates, and we apply a shallow layer model at the flow front to show how the initial mixture arrangement and proportion influence the effective coefficient of friction during emplacement. We find that a bidispersed mixture can induce a larger friction on emplacement than a monodispersed mixture, and the highest coefficient of friction was found for a well-mixed initial arrangement of particles at the proportion that shows maximum horizontal spreading of the flow. These observations suggest that downwards percolation of fine particles takes place at the front of the collapsing column, and so localised size segregation processes at the flow front can control flow mobility. This effect is likely to be important in controlling the mobility of large geophysical flows that occur on finite time scales, and whose deposits typically show granular segregation at the front and edges but not throughout the entire deposit

Mathematical modeling of powder-snow avalanche flows

Powder-snow avalanches are violent natural disasters which represent a major risk for infrastructures and populations in mountain regions. In this study we present a novel model for the simulation of avalanches in the aerosol regime. The second scope of this study is to get more insight into the interaction process between an avalanche and a rigid obstacle. An incompressible model of two miscible fluids can be successfully employed in this type of problems. We allow for mass diffusion between two phases according to the Fick's law. The governing equations are discretized with a contemporary fully implicit finite volume scheme. The solver is able to deal with arbitrary density ratios. Several numerical results are presented. Volume fraction, velocity and pressure fields are presented and discussed. Finally we point out how this methodology can be used for practical problems.Comment: 27 pages, 13 figures. Minor changes. A few references were added. Other author's papers can be downloaded at http://www.lama.univ-savoie.fr/~dutykh

Isothermal flow of an anisotropic ice sheet in the vicinity of an ice divide

Simulations of glacier flow are commonly based on the assumption that ice has an isotropic viscosity. Here we examine the plane flow of ice in the special region of an ice divide using a constitutive relation for an anisotropic, incompressible viscous body that is orthotropic and transversally isotropic. Ice is assumed to be isotropic at the ice sheet surface, with the continuous development of a vertical. single maximum c axis fabric with increasing depth. We consider the theoretical case of an: isothermal ice sheet over a horizontal bedrock, with no slip at the ice-bedrock interface. The ice sheet surface elevation is imposed, and the flow corresponding to the steady state is calculated, using a two-dimensional finite difference model based on the resolution of a pressure-Poisson equation. In this model, all components of the stress and strain rate tensor are calculated. The main conclusion is that for a fixed surface elevation, the general flow pattern accelerates when the anisotropic behavior of the ice is taken into account due to the greater fluidity with respect to shear stress. The downward motion of the ice is faster, despite a higher resistance to vertical deformation. As a result, the dominance of shear strain rate in the flow of polar ice is stronger in the anisotropic case than in the isotropic case. The shear stresses are slightly relaxed, while the longitudinal stresses are significantly increased in the anisotropic case