What is it about?
Gravity mass flows, such as avalanches or debris flows, can erode the substrate and thereby multiply their mass. This can have a very strong effect on the velocity and run-out distance of the flow. The mechanics of erosion is still poorly understood, and modellers use ad hoc assumptions to capture this process. This paper shows that the properties of the substrate and the flowing mass determine how much material the flow entrains. Thus, in reality there is no freedom in choosing the erosion model. In a few simplified situations, we were able to deduce the correct expression for the erosion rate from the material properties.
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Why is it important?
In the mitigation of natural hazards like snow avalanches, debris flows or quick-clay slides, numerical run-out models play an important role. In the past 20 years, they have become increasingly sophisticated. However, for some time to come, fully 3D simulations of large flows will remain impractical. Therefore, most models are only quasi-3D in that they average the flow over the dimension normal to the slope. This is most often a perfectly adequate simplification, but requires the bed friction and the erosion rate to be modelled as boundary conditions. In the absence of a deeper understanding of the mechanics of erosion, a vast number of heuristic expressions for the erosion rate as a function of different variables like the average flow speed or the shear stress have been used in the past. This paper cautions that these expressions typically will be inconsistent with the assumed flow law and substrate properties. Consistent analytic solutions can be found in a few simple settings, but beyond those one should infer useful approximations from numerical models that resolve the flow in the bed-normal direction, as e.g. shown in (Issler and Pastor 2011, Annals Glaciol. 52, 143‒147) or (Eglit and Yakubenko 2014, Cold Reg. Sci. Technol. 108, 139‒148).
Perspectives
This paper represents a first step in the development of consistent entrainment formulas for use in depth-averaged flow models of gravity mass flows in that it explicitly constructs such formulas without user-adjustable coefficients (besides the material properties that are assumed to be known a priori). These formulas apply only to a small class of relatively simple flow rheologies and are applicable only in a limited range of flow conditions. The analytic results obtained in the paper hint at the existence of a different erosion/entrainment regime where the bed material is too weak to resist deep, catastrophic erosion, but the flow is too weak to entrain the eroded material at once. It will be an exciting task to construct models describing this situation, and it is expected to make the model more applicable to many types of gravity mass flows in Nature. In fact, measurements on snow avalanches hint at the existence of such a more violent erosion regime, hypothesized and termed "ripping" by Gauer and Issler (2004). Another venue to follow is frontal, plowing entrainment. In the early Soviet literature on avalanche models, such an entrainment term was included as a jump condition for mass and momentum at the front of the flow and used to determine the shock propagation velocity. It will be interesting to extend this approach to determine the frontal erosion depth in a self-consistent manner. Also, while Eglit's shock front approach assumes a jump in the flow depth at the front, in reality the internal friction angle in the flow should limit how steep the front can be, and this should have an impact on the erosion depth. Grigorian and Ostroumov (1977) modified the concept of frontal entrainment by inclining the shock front between intact snow cover and moving avalanche so that the model describes basal entrainment. It seems, though, that only the jump conditions of the interface-normal component of momentum have been used by these authors. Moreover, it is unclear whether they determine the inclination of the interface dynamically or not. A thorough investigation of this system promises important insight into the general constraints on entrainment because the Grigorian–Ostroumov model is essentially independent of the rheology of the flowing material.
Dieter Issler
Norwegian Geotechnical Institute
Read the Original
This page is a summary of: Dynamically consistent entrainment laws for depth-averaged avalanche models, Journal of Fluid Mechanics, October 2014, Cambridge University Press,
DOI: 10.1017/jfm.2014.584.
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