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The principle of minimum entropy production and snow structure

  • Perry Bartelt (a1) and Othmar Buser (a1)

Abstract

An essential problem in snow science is to predict the changing form of ice grains within a snow layer. Present theories are based on the idea that form changes are driven by mass diffusion induced by temperature gradients within the snow cover. This leads to the well-established theory of isothermal- and temperature-gradient metamorphism. Although diffusion theory treats mass transfer, it does not treat the influence of this mass transfer on the form — the curvature radius of the grains and bonds — directly. Empirical relations, based on observations, are additionally required to predict flat or rounded surfaces. In the following, we postulate that metamorphism, the change of ice surface curvature and size, is a process of thermodynamic optimization in which entropy production is minimized. That is, there exists an optimal surface curvature of the ice grains for a given thermodynamic state at which entropy production is stationary. This state is defined by differences in ice and air temperature and vapor pressure across the interfacial boundary layer. The optimal form corresponds to the state of least wasted work, the state of minimum entropy production. We show that temperature gradients produce a thermal non-equilibrium between the ice and air such that, depending on the temperature, flat surfaces are required to mimimize entropy production. When the temperatures of the ice and air are equal, larger curvature radii are found at low temperatures than at high temperatures. Thus, what is known as isothermal metamorphism corresponds to minimum entropy production at equilibrium temperatures, and so-called temperature-gradient metamorphism corresponds to minimum entropy production at none-quilibrium temperatures. The theory is in good agreement with general observations of crystal form development in dry seasonal alpine snow.

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Copyright

References

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Bartelt, P and Lehning, M.. 2002. A physical SNOWPACK model for the Swiss avalanche warning. Part I. Numerical model. Cold Reg. Sci. Technol., 35(3), 123-145.
Bartelt, P., Buser, O. and Sokratov, S.. 2004. A non-equilibrium treatment of heat and mass transfer in alpine snowcovers. Cold Reg. Sci. Technol., 39(2-3), 219-242.
Bejan, A. 1996. Entropy generation mimimization. Boca Raton, FL, CRC Press.
Bejan, A. 1997. Advanced engineering thermodynamics. Second edition. New York, John Wiley and Sons.
Bejan, A. 2000. Shape and structure, from engineering to nature. Cambridge, Cambridge University Press.
Bozhinskiy, A. N. and Losev, K. S.. 1998. The fundamentals of avalanche science. Eidg. Inst. Schnee- und Lawinenforsch. Mitt. 55. (Translated from Russian by C. E. Bartelt)
Brun, E., Sudul, P, David, M. and Brunot, G.. 1992. A numerical model to simulate snow-cover stratigraphy for operational avalanche forecasting. J Glacial., 38(128), 13-22.
Buser, O. and Good, W.. 1987. Acoustic, geometric and mechanical parameters of snow. International Association of Hydrological Sciences Publication 162 (Symposium at Davos 1986 – Avalanche Formation, Movement and Effects), 61-71.
Colbeck, S. C. 1983. Theory of metamorphism of dry snow. J. Geophys. Res., 88(C9), 5475-5482.
Colbeck, S. C. 1987. A review of the metamorphism and classification of seasonal snow cover crystals. International Association of Hydrological Sciences Publication 162 (Symposium at Davos 1986 – Avalanche Formation, Movement and Effects), 3-34.
Coleman, B. D. and Noll, W.. 1963. The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Rat. Mech. Anal. 13(3), 167-178.
Glansdorf, P and Prigogine, I.. 1974. Thermodynamics theory of structure, stability and fluctuations. London, Wiley-Interscience.
Gubler, H. 1985. Model for dry snow metamorphism by interparticle vapor flux. J Geophys. Res., 90(D5), 8081-8092.
Incropera, F. P and DeWitt, D. P. 2002. Fundamentals of heat and mass transfer. Fourth edition. New York, etc., John Wiley and Sons.
Jaynes, E. 1980. The minimum entropy production principle. Ann. Rev. Phys. Chem., 31, 579-601.
Kaviany, M. 1995. Principles of heat transfer in porous media. Second edition. New York, etc., Springer-Verlag.
Lehning, M., Bartelt, P, Brown, B., Fierz, C. and Satyawali, P. 2002. A physical SNOWPACK model for the Swiss avalanche warning. Part II. Snow microstructure. ColdReg. Sci. Technol., 35(3), 147-167.
Marbouty, D. 1980. An experimental study of temperature-gradient metamorphism. J. Glacial., 26(94), 303-312.
McClung, D. M. and Schaerer, P. A.. 1993. The avalanche handbook. Seattle, WA, The Mountaineers.
Miller, D. 2002. An integrated microstructural study of dry snow metamorphism under generalized thermal conditions. (Ph.D. thesis, Montana State University.)
Prigogine, I. 1980. From being to becoming. San Francisco, W. H. Freeman and Company.
Shimizu, H. 1970. Air permeability of deposited snow. Contrib. Inst. Low Temp. Sci., Ser. A, 22, 1-32.
Sokratov, S. 2001. Parameters influencing the recrystallization rate of snow. ColdReg. Sci. Technol., 33(2-3), 263-274.

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