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 J. Sib. Fed. Univ. Math. Phys., 2021, Volume 14, Issue 1, Pages 47–56 (Mi jsfu890)

Mathematical model of fluids motion in poroelastic snow-ice cover

Margarita A. Tokareva, Alexander A. Papin

Altai State University, Barnaul, Russian Federation

Abstract: The dynamics of a snow-ice cover is considered within the theory of poroelasticity. The snow-ice cover is modeled by a three-phase medium consisting of water, air and ice. The governing equations are the equations of mass conservation for each phase with phase transitions, the equations of conservation of phase momentum in the form of Darcy's law, the equation of conservation of momentum of the whole system, the rheological equation for porosity and the equation of heat balance of snow. In the full formulation the liquid and air pressures are functions of the temperature and the corresponding densities, and the viscosity and compressibility coefficients of ice are functions of the temperature. The problem of two-dimensional nonstationary filtration of water in a thin poroelastic ice plate is considered in the model case. The solution is obtained in quadratures.

Keywords: poroelasticity, porosity, snow-ice cover, thin layer.

 Funding Agency Grant Number Ministry of Science and Higher Education of the Russian Federation MK-204.2020.1 The work was carried out under the project MK-204.2020.1 "Initial-boundary value problems for the equations of fluid motion in poroelastic media and their applications in the dynamics of snow and ice cover" with the support of a grant from the President of the Russian Federation.

DOI: https://doi.org/10.17516/1997-1397-2021-14-1-47-56

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UDC: 517.95
Accepted: 02.12.2020
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Citation: Margarita A. Tokareva, Alexander A. Papin, “Mathematical model of fluids motion in poroelastic snow-ice cover”, J. Sib. Fed. Univ. Math. Phys., 14:1 (2021), 47–56

Citation in format AMSBIB
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