Is there a universal log law for turbulent wall-bounded flows?

The history and theory supporting the idea of a universal log law for turbulent wall-bounded flows are briefly reviewed. The original idea of justifying a log law from a constant Reynolds stress layer argument is found to be deficient. By contrast, it is argued that the logarithmic friction law and velocity profiles derived from matching inner and outer profiles for a pipe or channel flow are well-founded and consistent with the data. But for a boundary layer developing along a flat plate it is not, and in fact it is a power law theory that seems logically consistent. Even so, there is evidence for at least an empirical logarithmic fit to the boundary-friction data, which is indistinguishable from the power law solution. The value of kappa approximately 0.38 obtained from a logarithmic curve fit to the boundary-layer velocity data, however, does not appear to be the same as for pipe flow for which 0.43 appears to be the best estimate. Thus, the idea of a universal log law for wall-bounded flows is not supported by either the theory or the data.     

The Savage-Hutter avalanche model: how far can it be pushed?

The Savage-Hutter (SH) avalanche model is a depth-averaged dynamical model of a fluid-like continuum implementing the following simplifying assumptions: (i) density preserving, (ii) shallowness of the avalanche piles and small topographic curvatures, (iii) Coulomb-type sliding with bed friction angle delta and (iv) Mohr-Coulomb behaviour in the interior with internal angle of friction phi> or =delta and an ad hoc assumption reducing the number of Mohr's circles in three-dimensional stress states to one. We scrutinize the available literature on information regarding these assumptions and thus delineate the ranges of validity of the proposed model equations. The discussion is limited to relatively large snow avalanches with negligible powder snow component and laboratory sand avalanches starting on steep slopes. The conclusion of the analysis is that the SH model is a valid model for sand avalanches, but its Mohr-Coulomb sliding law may have to be complemented for snow avalanches by a second velocity-dependent contribution. For very small snow avalanches and for laboratory avalanches starting on moderately steep and bumpy slopes it may not be adequate.     

Density variations in dry granular avalanches

Dry granular avalanches exhibit bulk density variations. Understanding the physical mechanisms behind these density variations is especially important in the study of geophysical flows such as snow and rock avalanches. We performed small-scale chute experiments with glass beads to investigate how bulk density changes, measuring velocity profiles, flow height and basal normal stress in an Eulerian measurement frame. The chute inclination and the starting volume of glass beads were systematically varied. From the flow height and basal normal stress data, we could compute the depth-averaged density at the measurement location during the passing of the avalanches. We observed that the depth-averaged density is not constant, varying with chute inclination and starting volume. Furthermore, the depth-averaged density varies from the head to the tail within a single avalanche. We model changes in density by accounting for the energy associated with the velocity fluctuations of the grains, the density and the velocity fluctuations being related by the constitutive relation for the normal stress. We propose expressions for the conduction and decay coefficients of the fluctuation energy which allow us to model the observed density variations in the experiments.     

Using AVAL-1D to simulate avalanches in the eastern Pyrenees

The two friction parameters used in the numerical avalanche dynamics program AVAL-1D, were calibrated empirically with data from observed avalanches in the Swiss Alps. The implementation of the model with these friction parameters in other regions with different characteristics can lead to considerable uncertainty if a previous calibration is not performed. However, direct calibration for a specific avalanche path is often not possible since the data available are insufficient. Therefore, we back-calculated twelve well-documented avalanche events from the Catalan Pyrenees to calibrate the friction coefficients to be used in this mountain range. The result of the study reveals that there is a good fit between recorded and simulated avalanche events using the friction parameters originally calibrated for the Swiss Alps, despite the difference in snow climate between these two mountain ranges.     

Rheology of a wet, fragmenting granular flow and the riddle of the anomalous friction of large rock avalanches

The effective friction coefficient of rock avalanches diminishes gradually as a function of the avalanche volume. Large rock avalanches can reach run-out distances as long as ten times the fall height, despite the fact that the physics of friction would indicate a run-out only a little greater than the fall height. Numerous suggestions have been put forward to explain this remarkable departure from the predictions of both small-scale experiments and basic theory. It is shown here that accounting for rock fragmentation within the avalanche in combination with the presence of water, leads to results in line with the data.     

颗粒接触摩擦系数空间变异性对颗粒流双轴数值试验的影响

提出了考虑颗粒摩擦系数空间变异性的砂土双轴剪切响应分析方法。采用随机场模型表征颗粒摩擦系数空间变异性,通过Karhunen-Loève展开方法离散接触摩擦系数随机场,编写了基于颗粒流程序PFC2D和MATLAB的随机模拟耦合分析程序。研究了摩擦系数空间变异性对密砂试样的双轴剪切响应影响规律。结果表明:1） 提出方法可有效地考虑颗粒间接触摩擦系数变异性对土体材料双轴压缩宏观力学行为影响;2） 密砂试样在剪切过程中的应力-应变关系曲线、体积-应变关系曲线的变化规律与颗粒间接触摩擦系数不确定性密切相关,在初始加载阶段随机模拟的偏应力曲线、体积应变曲线基本重合,继续加载后曲线开始发散;3） 垂直相关距离对峰值偏应力均值与标准差影响明显大于水平相关距离。颗粒接触摩擦系数的均值对峰值偏应力的影响大于摩擦系数空间分布的影响。摩擦系数的空间分布会影响剪切带的形成位置。     

The unacknowledged risk of Himalayan avalanches triggering

A “universal” model for avalanche triggering, as well as for collapse of suspended seracs, is presented based on Quantized Fracture Mechanics, considering fracture, friction, adhesion and cohesion. It unifies and extends the classical previous approaches reported in the literature, including the role of the slope curvature. A new size-effect, that on mountain height rather than the classical one on snow slab thickness, is also discussed and demonstrated thanks to glaciers data analysis from the World Glacier Inventory (http://nsidc.org/data/glacier_inventory/browse.html, 2014). The related most noteworthy result is that snow precipitation needed to trigger avalanches at 8,000 m could be up to 4 times, with a realistic value of 1.7 times, smaller than at 4,000 m. This super-strong size-effect may suggest that the risk of Himalayan avalanches is today still unacknowledged. A discussion on the recent Manaslu tragedy concludes the paper.     

Frictional behavior of granular gravel–ice mixtures in vertically rotating drum experiments and implications for rock–ice avalanches

Rapid mass movements involving large proportions of ice and snow can travel significantly further downslope than pure rock avalanches and may transform into debris-flows as the ice melts and as water from the stream network or water-saturated debris is incorporated. Currently, ice is thought to have three distinctive effects: 1) reduction of the friction within the moving mass itself, 2) increase of pore pressure as the ice melts and consequent reduction of the shear resistance of the flowing material, and 3) reduction of boundary friction where the failing mass travels on a glacier. However, measurement-based evidence to support these hypotheses is largely missing. In this study, laboratory experiments on the first two mechanisms were carried out in two partially-filled large rotating drums, one in Vienna (Austria) and a second in Berkeley (USA). Varying proportions of cold gravel and gravel-sized ice were mixed and added to the rotating drum running at constant rotational velocity until all ice had melted. Flow behavior was recorded with flow depth, normal force, shear force, pore-water pressure, and temperature sensors. The bulk friction coefficient was found to decrease linearly with increasing ice content by ~ 20% in the early phase of the experiments, before significant portions of the ice transformed into water. For ice contents larger than 40% by volume, the transformation from a dry granular flow to debris-flow-like movement or hyperconcentrated flow was observed when pore-water pressures rose and approached the normal forces along the flow profile. Pore-water pressure from melting ice developed within several minutes after the start of the experiments and, as it increased, progressively reduced the friction coefficient. The results emphasize that the presence of ice in granular moving material can significantly reduce the friction coefficient of both dry and partially-saturated debris. Due to size effects and the absence of other factors reducing friction (e.g. surfaces with low friction and rock comminution), the absolute measured friction coefficients from the laboratory experiments were larger than those found from natural events. However, the relative changes in friction coefficients depending on the ice and water content may also be considered in real-scale hazard assessments of rapid mass movements in high mountain environments.     

Modelling soil removal from snow avalanches: A case study in the North-Western Italian Alps

Snow avalanches can exert considerable erosive forces on soils. If a snow avalanche flows directly over bare ground, basal shear forces may scrape away and entrain soil. Sediments mix up with the avalanche body and may be found within the run-out snow deposit. Based on a previous field campaign aiming to quantify the amount of sediments trapped within avalanche bodies for the study site of Lavancher, in the Aosta Valley, NW-Italy, we developed here a soil erosion model, which we preliminarily applied to that site. An already developed and tested 1-D avalanche dynamics model was modified to include soil erosion. Soil removal was triggered according to two different mechanisms, namely excess of shear and critical velocity. We used equations from the available literature to model the shear stress exerted by the avalanche flow upon the ground underneath. Critical threshold for soil removal of either shear or velocity were also retrieved from the available literature, possibly depending upon soil texture and geotechnical properties. The model performs well in reproducing soil removal for three wet-dense avalanches that occurred in the study site.Use of excess of shear mechanism to evaluate erosion seems more robust, as less dependent upon flow velocity, utmost uncertain. Albeit more accurately measured events of soil eroding avalanches seem necessary to test its performance, the model can be used henceforth as a basis for further refinement concerning geomorphologic contribution of avalanches.     

Jamming in granular shear flows of frictional,polydisperse cylindrical particles

In this work, frictional, cylindrical particle shear flows with different size distributions (monodisperse, binary, Gaussian, uniform) are simulated using the Discrete Element Method (DEM). The influences of particle size distribution and interparticle friction coefficient on the solid phase stresses, bulk friction coefficient, and jamming transition are investigated. In frictional dense flows, shear stresses rise rapidly with the increasing solid volume fraction when jamming occurs. The results suggest that at the jamming volume fraction, stress fluctuation and granular temperature achieve the maximum values, and the rate of the stress increase with increasing solid volume fraction approaches the peak value. Meanwhile, the degree of cylindrical particle alignment approaches a valley value. In the polydisperse flows, the jamming volume fraction exhibits significant dependences on the fraction of the longer particles and the particle size distribution. Two models considering the effect of particle size distribution are discussed for predicting the jamming volume fractions of polydisperse flows with frictional, cylindrical particles.     

On forecasting large and infrequent snow avalanches

Snow avalanches that threaten a highway or a residential area are often large avalanches that have a return period > 1 year. Danger assessment strongly relies on precipitation data since these avalanches are typically triggered by major snow storms. Given the extensive protection work that is in place in the European Alps, the avalanche control service (also called avalanche commission) responsible for danger assessment will usually monitor the avalanche situation throughout the winter, but only become active in case of a major snow fall. Related safety concepts describing the procedures and measures to be taken in a given danger situation are therefore often based on threshold values for new snow. By analysing the avalanche occurrence of a major avalanche path, we show that forecasting based on new snow amounts involves high uncertainty. Whereas the return period of an avalanche to, for example, the road was about 5 years, the return period for the corresponding new snow depth was substantially smaller, in our case slightly less than 2 years. Similar proportions were found for a number of other avalanche paths with different snow climate. The return period of the critical new snow depth was about 2–5 times smaller than the return period of the avalanche. This proportion is expected to increase with increasing return period. Hence, based on the return period of an avalanche path a first estimate for the critical new snow depth can be made. With a return period of the critical new snow depth of 1–2 years, avalanche prediction for individual avalanche path becomes very challenging since the false alarm ratio is expected to be high.     

On forecasting large and infrequent snow avalanches

Snow avalanches that threaten a highway or a residential area are often large avalanches that have a return period > 1 year. Danger assessment strongly relies on precipitation data since these avalanches are typically triggered by major snow storms. Given the extensive protection work that is in place in the European Alps, the avalanche control service (also called avalanche commission) responsible for danger assessment will usually monitor the avalanche situation throughout the winter, but only become active in case of a major snow fall. Related safety concepts describing the procedures and measures to be taken in a given danger situation are therefore often based on threshold values for new snow. By analysing the avalanche occurrence of a major avalanche path, we show that forecasting based on new snow amounts involves high uncertainty. Whereas the return period of an avalanche to, for example, the road was about 5 years, the return period for the corresponding new snow depth was substantially smaller, in our case slightly less than 2 years. Similar proportions were found for a number of other avalanche paths with different snow climate. The return period of the critical new snow depth was about 2–5 times smaller than the return period of the avalanche. This proportion is expected to increase with increasing return period. Hence, based on the return period of an avalanche path a first estimate for the critical new snow depth can be made. With a return period of the critical new snow depth of 1–2 years, avalanche prediction for individual avalanche path becomes very challenging since the false alarm ratio is expected to be high.     

Simple physical model for the fragmentation of rock avalanches

Rock avalanches are the largest granular flows on Earth. In contrast to artificial, small-scale granular avalanches, they exhibit a large degree of fragmentation with reduction of average grain volume by a factor of up to 10¹⁵–10¹⁸. Even though fragmentation likely affects the whole dynamics of the rock avalanche, as yet the basic mechanics of the process is poorly known. In this work, a simple model is presented for the fragmentation of rock avalanches, assuming that most of the fragmentation occurs along force chains in the granular medium. The landslide motion is simulated along a curved bumpy profile path. The predicted grain spectra are found to agree reasonably with field data.     

Thermohaline considerations in surface gravity driven flows

Surface gravity driven currents of varying scales play a major role in both natural and human-made settings. The driving buoyancy forces for these flows are due to horizontal density gradients that may be due to compositional differences across an interface arising from salinity or temperature contrasts. These density gradients may also arise due to the presence of suspended solid material in the current as in the case of turbidity currents, pyroclastic flows or powder snow avalanches. In this article we will model a class of surface gravity flows wherein the density gradients are due to surface fluxes of both heat and salinity. With the assumption of low aspect ratio flows we employ the two-layer shallow water equations wherein the density of the upper layer is specified by a general equation of state involving both salinity and temperature. In all cases we consider fixed volume releases of lighter fluids into heavier ambient fluids whose properties remain unchanged. The complex dynamics of these two-layer systems is investigated using distinguished-limit models combined with a variety of analytical methods, as well as, numerical schemes.     

An investigation of radiation-recrystallization coupling laboratory and field studies

Near-surface faceted crystals are often attributed as being the weak-layer in fatal slab avalanches. To gain a further understanding of these crystals Montana State University researchers collaborated with the Yellowstone Club Ski Patrol to investigate near-surface metamorphism. Detailed weather information as well as daily observations and grain-scale images were collected from January to April, 2008. Several radiation-recrystallization events were observed throughout this period. Near-surface facets were successfully developed using laboratory simulations of recorded field data. A comparison of measured data with a thermal model indicated that natural snow would likely have higher temperature gradients compared to the laboratory snow test given the same environmental conditions. This phenomenon indicates that low-density snow may be conducive, but not obligatory, to form near-surface facets. This work highlights that field and laboratory investigations may be coupled to reveal information not present in the individual studies alone.     

A semi-empirical re-evaluation of the influence of state on elastic stiffness in granular materials

Granular Matter - The calculation of the impact pressure on obstacles in granular flows is a fundamental issue of practical relevance, e.g. for snow avalanches impacting obstacles. Previous...     

Fuzzy modelling of powder snow avalanches

This paper examines powder snow avalanches by introducing a predetermined degree of variation, or fuzziness, in model parameters. Given a value of vagueness in the parameters, fuzzy set theory makes it possible to evaluate the vagueness in the results. The use of a more complex stochastic analysis can be avoided. Six parameters of the model are taken to be affected by a certain amount of uncertainty; the response of the numerical model is calculated by solving the fuzzy equations. In this way, it is possible to evaluate how the results are affected by a given change in the model parameters.The paper first presents a well-known avalanche model and its solution considering the influence of friction. A brief introduction of the fuzzy set is given with regard to the avalanche model mentioned. Later, the fuzzy solution of the model in terms of velocity and average pressure is calculated for three different levels of imprecision in the data. At the end, the results are presented and commented.     

High-speed video recording of basal shear layers in snow chute flows

Run-out distances and flow velocities of snow avalanches are mainly determined by frictional processes originating from the interaction with the ground. At the SLF snow chute at the Weissfluhjoch near Davos, a setup was developed which allowed us to record high-speed movies of the basal shear layer of small-scale avalanches with a frame rate of 1000 frames per second. Shear processes could be observed in high-resolution slow motion. Downstream velocity profiles were extracted by a pattern matching algorithm. The comparison of computed profiles with velocity profiles obtained from optical sensors showed good agreement. However, the temporal and spatial resolutions are much higher for the high-speed video data. Because the optical velocity sensors are one-dimensional, we found that they overestimate the velocities when a flow-normal velocity component exists as well. All measured velocity profiles exhibited very high shear rates near the ground. The maximum shear rates were up to 600/s for dry snow and 200/s for wet snow avalanches. The observations of the video images suggested a turbulent motion of the snow in the basal shear layer.     

Remote sensing of snow accumulation

New snow depth provides a valuable tool for forecasting avalanches. We have modified an ultrasonic rangefinder available from Polaroid, and have mounted the unit at the top of a tripod. By taking hourly measurements, the changes in distance between the transducer and the snowpack can be evaluated. Blowing snow during storms shows up as scattered data, and at the end of a storm the readings become stable. The data indicate the length of the storm as well as the new snow increment.