Tracking the free surface of time-dependent flows: image processing for the dam-break problem

The dam-break problem (i.e., the sudden release of a given volume of fluid down a slope) has attracted a great deal of attention from mechanicians and physicists over the past few years, with particular interest devoted to the free-surface profile and the spreading rate. Experimentally, impediments to accurate measurements of the free-surface evolution are numerous because of the significant variations in its curvature and velocity. To accurately measure the surge's free-surface variations with time, we have developed a new imaging system, consisting of a digital camera coupled with a synchronized micro-mirror projector. The object's surface is imaged into a camera and patterns are projected onto the surface under an angle of incidence that differs from the imaging direction. From the deformed pattern recorded by the camera, the phase can be extracted and, by using unwrapping algorithms, the height can be computed and the free surface reconstructed. We were able to measure the free surface of the flow to within 1mm over a surface of 1.8 × 1.1m2. Although the techniques used in our system are not new when taken individually, the system in its entirety is innovative and more efficient than most methods used to-date in practical application

Why don't avalanche-dynamics models of higher complexity necessarily lead to better predictions?

The avalanche-dynamics approach has a long history in avalanche prediction. In the absence of computers, scientists and engineers focused on idealized models in which avalanches were seen as rigid sliding blocks. Although the resulting governing equation was very simple, the use of empirical rules made the model outcomes quite realistic, the errors being counterbalanced by common sense and experience of practitioners. To improve the earliest models, scientists explored two complementary paths. The first was to provide a more physical framework for avalanches. In the 1960s, Bruno Salm suggested that flowing snow can be regarded as a continuum, an idea which has encountered great success, but which, at that time, faced considerable computational difficulties. A second path was the development of analytical and numerical models to solve the governing equations of continuum models. In the 1970s, French and Soviet scientists played a key role in the development of the Saint-Venant models for flowing avalanches. Since the 1990s, these models have been made available worldwide.Paradoxically, the substantial increase in model complexity can lead us to lose sight of the empirical nature of the assumptions used to build the models. Human expertise should still be of paramount importance when evaluating the relevance of numerical outputs. In 2004, Salm sounded an alarm, stating that excessive confidence was placed in the accuracy of model outputs. The problem of predictability and accuracy of models used for environmental purposes has attracted growing attention in recent years, but the debate seems an endless story as it is extremely difficult to determine the source of errors and remove them.In this talk, I will present the conclusions of experimental campaigns conducted in the laboratory to study avalanches of fluid. In this setting, an avalanche of fluid results from the sudden release of a fixed volume of fluid down a sloping bed. Both flui d properties and flow geometry are imposed. Using high-resolution flow-visualization techniques, we are also able to monitor the internal evolution of the avalanche from release to runout. The experimental data can then be compared with models of varying complexity. For Newtonian fluids (i.e., fluids whose rheological behavior is linear), we have found that the model accuracy increases with its degree of complexity. Surprisingly, for viscoplastic fluids (non-linear rheology), simple models perform much better than sophisticated models (such as the Saint-Venant equations). Our conclusions do not differ from the lessons learnt in other fields, such as atmospheric sciences, in which small nonlinearities in the governing equations are known to produce large errors, which accumulate to give false predictions. There is no feasible reason why governing equations such as the Saint-Venant equations, which are unable to provide accurate predictions in well-controlled experiments should miraculously outperform other methods when applied to complex natural phenomena such as snow avalanches. Such models are certainly valuable in avalanche expertise as they provide a precise conceptual framework that link physical processes to universal principles such as conservation of mass and momentum. But, in agreement with Salm’s warning, our experiments show that the returns from using sophisticated models may be minimal or diminishing unless we take notice of the errors and biases introduced by these models

Stochastic modeling in sediment dynamics: Exner equation for planar bed incipient bed load transport conditions

Even under flow equilibrium conditions, river bed topography continuously evolves with time, producing trains of irregular bed forms. The idea has recently emerged that the variability in the bed form geometry results from some randomness in sediment flux. In this paper, we address this issue by using the Exner equation and a population exchange model derived in an earlier paper. In this model, particle entrainment and deposition are idealized as population exchanges between the stream and the bed, which makes it possible to use birth‐death Markov process theory to track the number of moving grains. The paper focuses on nascent bed forms on initially planar beds, a situation in which the coupling between the stream and bed is weak. In a steady state, the number of moving particles follows a negative binomial distribution. Although this probability distribution does not enter the family of heavy‐tailed distributions, it may give rise to large and frequent fluctuations because the standard deviation can be much larger than the mean, a feature that is not accounted for with classic probability laws (e.g., Hamamori’s law) used so far for describing bed load fluctuations. In the large‐system limit, the master equation of the birth‐death Markov process can be transformed into a Fokker‐Planck equation. This transformation is used here to show that the number of moving particles can be described as an Ornstein‐Uhlenbeck process. An important consequence is that in the long term, the number of moving particles follows a Gaussian distribution. Laboratory experiments show that this approximation is correct when the mean number per unit length of stream, $\vec{N}$/L, is sufficiently large (typically two particles per centimeter in our experiments). The particle number fluctuations give rise to bed elevation fluctuations, whose spectrum falls off like $\omega^{-2}$ in the high‐frequency regime (with $\omega$ the angular frequency) and variance grows linearly with time. These features are in agreement with recent observations on bed form development (in particular, ripple growth)

Les avalanches de neige

Les avalanches sont des écoulements rapides de neige sur une pente de montagne. Par extension, cela peut être des écoulements d’autres matériaux ; on parle parfois d’avalanche sous-marine ou d’avalanches de pierre. Le moteur de l’écoulement est la gravité. Les vitesses atteintes par une avalanche couvrent une large plage allant des faibles vitesses (quelques m/s) à des vitesses approchant celle d’un corps en chute libre (plus de 30 m/s). Les hauteurs d’écoulement sont également très variables : de quelques mètres pour des écoulements denses à plus de 100 m pour un écoulement dilué. Les distances parcourues sont également très variables : de quelques dizaines de mètres pour une petite coulée à plusieurs kilomètres pour les grosses avalanches mobilisant des volumes de plusieurs centaines de milliers de m3

Monte Carlo calibration of avalanches described as Coulomb fluid flows

The idea that snow avalanches might behave as granular flows, and thus be described as Coulomb fluid flows, came up very early in the scientific study of avalanches, but it is not until recently that field evidence has been provided that demonstrates the reliability of this idea. This paper aims to specify the bulk frictional behaviour of snow avalanches by seeking a universal friction law. Since the bulk friction coefficient cannot be measured directly in the field, the friction coefficient must be calibrated by adjusting the model outputs to closely match the recorded data. Field data are readily available but are of poor quality and accuracy. We used Bayesian inference techniques to specify the model uncertainty relative to data uncertainty and to robustly and efficiently solve the inverse problem. A sample of 173 events taken from seven paths in the French Alps was used. The first analysis showed that the friction coefficient behaved as a random variable with a smooth and bell-shaped empirical distribution function. Evidence was provided that the friction coefficient varied with the avalanche volume, but any attempt to adjust a one-to-one relationship relating friction to volume produced residual errors that could be as large as three times the maximum uncertainty of field data. A tentative universal friction law is proposed: the friction coefficient is a random variable, the distribution of which can be approximated by a normal distribution with a volume-dependent mean

Avalanches : phénomènes et enjeux.

Si les avalanches ne constituent pas un danger naturel majeur à l'échelle de la planète, elles représentent une menace et une contrainte fortes pour un pays montagneux comme la Suisse. Ce n'est donc pas un hasard si la Suisse a été la pionnière dans l'étude scientifique des avalanches avec les travaux d'un ingénieur forestier des Grisons, Johann Coaz, à la fin du XIXe siècle. Et c'est également sur le modèle suisse de zonage des risques - établi après le terrible hiver 1951 (98 morts) - que tous les pays occidentaux ont calqué leurs plans de zonage, c'est-à-dire les documents réglementaires planifiant de façon rationnelle l'utilisation du sol sur un territoire soumis à des dangers naturels. À l'heure ou prouesses de la technologie et réchauffement climatique peuvent laisser croire que les avalanches sont à ranger dans les terreurs du passé, il n'est pas inutile de faire le point sur notre connaissance des phénomènes et sur la gestion du risque dans notre pays et en Europe. Dans ma conférence, je donnerai un rapide aperçu sur la physique des avalanches : pourquoi un manteau neigeux peut donner naissance à une avalanche ? Comment s'écoule-t-elle ? Quelles sont ses caractéristiques ? Je m'appuierai essentiellement sur les dernières avancées, notamment celles permises par le site de la Vallée de la Sionne (VS) gérée par le WSL/SLF. La seconde partie de la conférence s'attaquera à la gestion du risque d'avalanche. Je dresserai un bilan du retour d'expérience après l'hiver 1999, où environ une soixantaine de personnes furent tuées dans leur habitation au cours du mois de février. Un problème crucial de notre société est de savoir comment faire face à la demande d'urbanisation croissante dans des secteurs que l'on sait exposés (l'essentiel du territoire peu ou pas exposé à des dangers naturels est déjà aménagé). Comment est-ce que la problématique scientifique peut trouver un écho dans les décisions des politiques ? Enfin, quand on sait que les Alpes souffrent plus que toute autre région de l'Europe continentale de la montée des températures, il est intéressant d'examiner ce que les projections actuelles nous prédisent quant à la persistance d'un manteau neigeux durant la saison hivernale et donc l'occurrence d'avalanches catastrophiques

Avalanche of fluid in the laboratory: the dam-break problem revisited.

The talk reviews some of the analytical results available for studying the dambreak problem. Emphasis is then given to a thorough comparison between experimental data, analytical results (lubrication theory), and numerical simulations (obtained using the shallow "water" equations) for Newtonian fluids, viscoplastic materials, and density-matched particle suspensions. We show that the front has a specific behavior, due to a large extent to the pronounced curvature of the free surface that causes the shear stress to significantly increase (relative to the behavior in the body), but surprisingly enough, the details of this front behavior are not essential to determining the flow behavior of the fluid avalanche. The last part of the talk is devoted to avalanches of particle suspensions, whose behavior is highly dependent on the particle concentration. In spite of particle migration (which causes a significant blunting of the velocity profile), the analogy with an equivalent homogeneous Newtonian fluid performs well for concentrations as large as 0.56, but for concentrations in excess of 0.58, a more complicated behavior including stick-slip motion is observed

Role of lubricated contacts in concentrated polydisperse suspensions

Synopsis In this article experimental results of the bulk behavior of concentrated suspensions of coarse and fine ͑colloidal͒ particles in a Newtonian fluid ͑water͒ are presented. Different rheological behaviors can be observed depending on both the solid concentrations in fine and coarse particles and the shear velocity. For suspensions concentrated in coarse particles that are poor in fine particles, the bulk behavior is frictional for low shear velocities and viscous for sufficiently large shear velocities. In the converse case, for mixtures rich in fine particles, the bulk behavior is viscoplastic. A more complex time-dependent behavior can be observed when the viscoplastic force exerted by the dispersion on coarse particles roughly balances the force of gravity. The diversity in bulk behavior is explained by the specific role played by the contact between coarse particles