Points of current interest in the Grigorian–Ostroumov avalanche model from the 1970s

What is it about?

Two decades before the development of numerical avalanche simulation models in the West, Soviet researchers had already developed numerical flow models for snow avalanches, extending concepts from hydraulics like the shallow-water approximation and adding advanced models for snow entrainment. These models were also calibrated and extensively tested against dedicated avalanche experiments in the Khibiny Mountains and the Caucasus. Strangely, these break-throughs were hardly noticed in the West, despite a (small) number of publications in English. In 1996, the late S. S. Grigorian held a talk on one of these models during a symposium in Davos, Switzerland, and submitted a paper for the planned proceedings, which, however, have never been published. In the context of a Special Issue on snow avalanche dynamics in the journal Geosciences, the manuscript was finally published in an edited form in 2020 (Geosciences 10, 35, DOI: 10.3390/geosciences10010035) because it is not only of considerable historical importance, but also proposes solutions to several issues that are still of current interest―the merits and limitations of simple analytical models, the apparently lower friction in very large avalanches, consistent and parameter-free modeling of basal snow entrainment, and hints of non-monotonicity of the run-out distance in the friction coefficients for complex friction models combined with entrainment. The present paper was written to document and explain the editorial changes to the original manuscript and to briefly discuss the possible impact of Grigorian and Ostroumov's work for current research on snow avalanche models.

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Photo by Krzysztof Kowalik on Unsplash

Photo by Krzysztof Kowalik on Unsplash

Why is it important?

The Comments paper addresses four main topics from Grigorian and Ostroumov's paper that are still worth pondering today: 1. Are analytically solvable simplifications of more complex avalanche models still of interest in 2020? The author's experience is that young researchers entering the field of avalanche dynamics often struggle due to the lack of intuition of what these complex equations actually do and whether numerical solutions are plausible or not. Grigorian and Ostroumov's paper can be valuable material in courses or self-study because it shows very explicitly how simplified versions of complex models can be derived, how they can be solved analytically, and what their limitations are. This aspect has been largely forgotten with the advent of comprehensive software packages for avalanche simulation, and there have been a number of unqualified uses of these models in critical hazard-mapping applications. 2. Is Grigorian's stress-limited friction law of interest in avalanche modeling? In 1979, Grigorian proposed a very simple solution to a ling-standing conundrum in landslide research: Why does the run-out angle (or, equivalently, the apparent friction coefficient) decrease to extremely low values with increasing landslide volume? He proposed that the bed shear stress in a landslide has a (material-dependent) upper limit so that the effective friction coefficient decreases inversely as the overburden increases. The present paper discusses under which circumstances an upper limit to the shear stress might arise. It is suggested that Grigorian's heuristic friction law might be able to capture much or all of the volume dependence in empirical calibrations of Voellmy-type snow avalanche models, even though it does not directly capture the complex processes that determine friction in avalanche flows. 3. Can the Grigorian–Ostroumov erosion model be used in modern avalanche flow models? The Grigorian–Ostroumov erosion model is one of the very few models of its kind that is based on a clear physical description of the process as a propagating shock and is (essentially) devoid of empirical parameters. The erosion rate is determined in terms of the density and strength of the snow cover, and the density, depth and velocity of the avalanche. This makes it a very attractive candidate for inclusion in modern models as well. There are, however, a few loose ends in the terse description of the model in the original paper. The present Comments paper addresses these issues by comparing the Grigorian–Ostroumov model to two conceptually related entrainment models, namely the frontal entrainment model by Eglit, Grigorian and Yakimov, and the tangential-jump entrainment model discussed by T. Jóhannesson and the author. This comparison allowed to largely clarify these issues and to outline ways for further refining the Grigorian–Ostroumov erosion model. 4. Is the run-out of avalanches non-monotonous in the friction parameters? In numerical simulations with the complete model, including entrainment and Grigorian's stress-limited friction law, Grigorian and Ostroumov observed "ignition" of the avalanche flow in a limited range of the dry-friction coefficient μ, whereas the flows slowed down and stopped for values of μ both above and below this range. If such non-monotonicity indeed is a general feature of reasonably realistic (thus, relatviely complex) avalanche flow models, the reliability and predictive power of such models and their applicability to real-world avalanche hazard mapping are put in doubt. The present paper cannot answer this question. However, a simplified system of equations is proposed that likely also would exhibit non-monotonicity, but is more amenable to mathematical analysis and a thorough exploration of its phase structure.

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