Abstract
A mathematical description of the processes of diffusion heat and mass transfer in a freezing seminfinite layer of seawater is presented. The mathematical formulation of a version of Stefan’s problem accounts for the possibility of the formation of a zone of phase transitions beyond which no phase transitions take place and the phase composition is known. Within the frameworks of a one-dimensional case and under a series of simplifying assumptions, self-similar solutions of the problem were obtained and plotted, such as the temperature and salinity distributions in the ice and the sub-ice layer, the phase composition of the sea ice, the heat flux across its upper boundary, and the position of the phase transition front. A qualitative comparison of these results with the experimental data available is presented.
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References
D. V. Aleksandrov, “Influence of the Concentrational Overcooling on the Morphological Stability of the Self-Similar Process of Solidification with a Flat Front,” Dokl. Ros. Akad. Nauk 179(1), 33–37 (2001).
V. I. Vasil’ev, A. M. Maksimov, E. E. Petrov, and G. G. Tsypkin, Heat and Mass Transfer in Freezing and Thawing Grounds (Nauka, Moscow, 1997) [in Russian].
S. N. Dikarev, S. G. Poyarkov, and S. I. Chuvil’nikov, “Laboratory Modeling of Small-Scale Convection Under a Growing Ice Cover in Winter Arctic Leads,” Okeanologiya 49(1), 70–79 (2004) [Oceanology 49 (1), 62–70 (2004)].
Yu. P. Doronin and N. V. Kubyshkin, Growth and Thawing of Sea Ice (Gidrometeoizdat, St. Petersburg, 2001) [in Russian].
A. P. Makshtas, Heat Balance of Arctic Ice in the Winter Period (Gidrometeoizdat, Leningrad, 1984) [in Russian].
Yu. L. Nazintsev and V. V. Panov, Phase Composition and Thermophysical Characteristics of Sea Ice (Gidrometeoizdat, St. Petersburg, 2000) [in Russian].
A. Ya. Ryvlin, “Method for Forecasting the Bending Strength Limit of the Ice Cover,” Probl. Arkt. Antarkt., No. 45, 79–86 (1974).
V. L. Tsurikov, Liquid Phase in Sea Ice (Nauka, Moscow, 1976) [in Russian].
N. G. Yakovlev, “A Coupled Model for the General Water Circulation and Evolution of Sea Ice in the Arctic Ocean,” Izv. Akad. Nauk, Fiz. Atmos. Okeana 39(3), 394–409 (2003).
P. W. Emms and A. C. Fowler, “Compositional Convection in the Solidification of Binary Alloys,” J. Fluid Mech. 262, 11–39 (1994).
R. S. Kerr, A. N. Woods, M. G. Worster, and H. E. Huppert, “Solidification of an Alloy Cooled from Above. Part 1. Equilibrium Growth,” J. Fluid Mech. 216, 323–342 (1990).
J. S. Wettlaufer, “Introduction to Crystallization Phenomena in Sea Ice,” in IAPSO Advanced Study Institute—Summer School: Physics of Ice-Covered Seas, Ed. by M. Leppäranta (University of Helsinki, 1998), pp. 105–194.
M. G. Worster, “Solidification of an Alloy from a Cooled Boundary,” J. Fluid Mech. 167, 481–501 (1986).
M. G. Worster, “The Dynamics of Mushy Layers,” in Interactive Dynamics of Convection and Solidification, NATO ASI E219, Ed. by S. H. Davis et al. (Kluwer, 1992), pp. 113–138.
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Original Russian Text © P.V. Bogorodskii, A.V. Pnyushkov, 2006, published in Okeanologiya, 2006, Vol. 46, No. 1, pp. 21–26.
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Bogorodskii, P.V., Pnyushkov, A.V. On the heat and mass transfer at the initial stage of ice formation in the sea. Oceanology 46, 17–22 (2006). https://doi.org/10.1134/S0001437006010036
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DOI: https://doi.org/10.1134/S0001437006010036