An energy-based method to calculate streamwise density variations in snow avalanches

Snow avalanches are gravity-driven flows consisting of hard snow/ice particles. Depending on the snow quality, particularly temperature, avalanches exhibit different flow regimes, varying from dense flowing avalanches to highly disperse, mixed flowing-powder avalanches. In this paper we investigate how particle interactions lead to streamwise density variations, and therefore an understanding of why avalanches exhibit different flow types. A basic feature of our model is to distinguish between the velocity of the avalanche in the mean, downslope direction and the velocity fluctuations around the mean, associated with random particle movements. The mechanical energy associated with the velocity fluctuations is not entirely kinetic, as particle movements in the slope-perpendicular direction are inhibited by the hard boundary at the bottom giving rise to a change in flow height and therefore change in flow density. However, this volume expansion cannot occur without raising the center of mass of the particle ensemble, i.e. an acceleration, which, in turn, exerts a pressure on the bottom, the so-called dispersive pressure. As soon as the volume no longer expands, the dispersive pressure vanishes and the pressure returns to the hydrostatic pressure. Different streamwise density distributions, and therefore different avalanche flow regimes, are possible.

Dispersive pressure and density variations in snow avalanches

Snow avalanches possess two types of kinetic energy: the kinetic energy associated with the mean velocity in the downhill direction and the kinetic energy associated with individual particle velocities that vary from the mean. The mean kinetic energy is directional; the kinetic energy associated with the velocity fluctuations is non-directional in the sense that it is connected to random particle movements. However, the rigid, basal boundary directs the random fluctuation energy into the avalanche. Thus, the random energy flux is converted to free mechanical energy which lifts and dilates the avalanche flow mass, changing the flow density and increasing the normal (dispersive) pressure and, as a consequence, changing the flow resistance. In this paper we derive macroscopic relations that link the production of the random kinetic energy to the perpendicular acceleration of the avalanche’s center of mass. We show that a single burst of fluctuation energy will produce pressures that oscillate around the hydrostatic pressure. Because we do not include a damping process, the oscillations of the center of mass remain, even if the production of random kinetic energy stops. We formulate relationships that can be used within the framework of depth-averaged mass and momentum equations that are often used to simulate snow avalanches in realistic terrain.

Geochemical evolution of a 10 m-thick intrusive body: the South Brenterc’h diabase dyke, Western Armorican Massif, France

The South Brenterc’h 9.5 m-thick diabase dyke belongs to the intermediate-Ti quartz-normative tholeiitic magmatism, which has intruded the western end of Britanny (France) near the Trias-Lias boundary. It has been previously identified as a "simple" dyke, resulting from a single magmatic injection. The present study is based on ten samples collected along a half transverse section of this dyke. Geochemical analyses and some textural parameters have been used to point out two flow-related differentiation processes, partially masked by alteration. These late magmatic mechanisms have induced subtle geochemical variations among samples, which sometime counteract each other. The processes pointed out here are (i) expulsion of phenocrysts from the borders during flow differentiation, likely by the way of an hydrodynamic grain dispersive pressure, and (ii) emplacement of a more evolved magma in the central part of the intrusion, probably due to a viscosity segregation mechanism during the flow.