Nonlinear dynamics of phase transitions during seawater freezing with false bottom formation / Alexandrov D.V., Malygin A.P. // Oceanology. - 2011. - V. 51, l. 6. - P. 940-948.

ISSN:
00014370
Type:
Article
Abstract:
This paper concerns mathematical modeling of the processes of false bottom evolution taking into account water freezing in the opposite direction from the cooled boundary with the atmosphere. The model of the crystallization process is based on the two-phase zone theory complicated by the moving boundaries of phase transitions and turbulent flows of fluid in the ocean near the false bottom boundary. Analytical solutions of the nonlinear problem are found (the distributions of the temperature and the salinity, the proportion of the solid fraction, the laws of the motion of the boundaries between the phase transitions, and the heat fluxes) and a comparative analysis of the results with the field data observations is performed. It is shown that the heat flux caused by the growing false bottom makes a significant contribution to the heat exchange processes between the ocean and the atmosphere. © 2011 Pleiades Publishing, Ltd.
Author keywords:
Index keywords:
air-sea interaction; analytical method; crystallization; freezing; heat flow; heat flux; numerical model; phase transition; seawater; turbulent flow
DOI:
10.1134/S0001437011060014
Смотреть в Scopus:
https://www.scopus.com/inward/record.uri?eid=2-s2.0-84155189640&doi=10.1134%2fS0001437011060014&partnerID=40&md5=17669ae6a311c46ecdbdde36fda533e3
Соавторы в МНС:
Другие поля
Поле Значение
Link https://www.scopus.com/inward/record.uri?eid=2-s2.0-84155189640&doi=10.1134%2fS0001437011060014&partnerID=40&md5=17669ae6a311c46ecdbdde36fda533e3
Affiliations Gor'ky Urals State University, Yekaterinburg, Russian Federation
References Alexandrov, D.V., Solidification with a Quasiequilibrium Two-Phase Zone (2000) Dokl. Akad. Nauk, 375 (2), pp. 172-176; Alexandrov, D.V., Malygin, A.P., Analytical Description of Seawater Crystallization in Ice Fissures and Their Influence on Heat Exchange between the Ocean and the Atmosphere (2006) Dokl. Earth Sci., 411 A (9), pp. 1407-1411; Alexandrov, D.V., Ivanov, A.A., Malygin, A.P., Self-Similar Solidification with a Two-Phase Zone of the Cooled Wall (2008) Vestn. Udmurt. Univ, 1, pp. 14-25; Alexandrov, D.V., Nizovtseva, I.G., Nonlinear Dynamics of the False Bottom during Seawater Freezing (2008) Dokl. Earth Sci., 419 (2), pp. 359-362; Borisov, V.T., Vinogradov, V.V., Dukhin, A.M., Applicability of the Theory of Quasi-Equilibrium Two-Phase Zone to Describing the Crystallization of an Ingot (1971) Izv. AN SSSR, Metally, 6, pp. 104-109; Zubov, I.N., (1945) Arctic Ice, , Moscow: Izd. Glavsevmorputi; Ivantsov, G.P., Diffusional Supercooling during Crystallization of a Binary Alloy (1951) Dokl. Akad. Nauk SSSR, 81 (2), pp. 179-182; Rubinshtein, L.I., (1967) Stefan's Problem, , Riga: Zvaigzne; Alexandrov, D.V., Solidification with a Quasiequilibrium Mushy Region: Exact Analytical Solution of Nonlinear Model (2001) J. Cryst. Growth, 222, pp. 816-821; Alexandrov, D.V., Aseev, D.L., Solidification of an Alloy with a Mushy Zone: Thermodiffusion and Temperature-Dependent Diffusivity (2005) J. Fluid Mech., 527, pp. 57-66; Alexandrov, D.V., Aseev, D.L., Directional Solidification with a Two-Phase Zone: Thermodiffusion and Temperature-Dependent Diffusivity (2006) Comput. Mater. Sci., 37 (1-2), pp. 1-6; Alexandrov, D.V., Malygin, A.P., Self-Similar Solidification of an Alloy from a Cooled Boundary (2006) Int. J. Heat Mass Transfer, 49, pp. 763-769; Alexandrov, D.V., Malygin, A.P., Alexandrova, I.V., Solidification of Leads: Approximate Solutions of Non-Linear Problem (2006) Ann. Glaciol., 44, pp. 118-122; Alexandrov, D.V., Aseev, D.L., Nizovtseva, I.G., Nonlinear Dynamics of Directional Solidification with a Mushy Layer. Analytic Solutions of the Problem (2007) Int. J. Heat Mass Transfer, 50, pp. 3616-3623; Alexandrov, D.V., Nizovtseva, I.G., To the Theory of Underwater Ice Evolution, or Nonlinear Dynamics of 'False Bottoms (2008) Int. J. Heat Mass Transfer, 51, pp. 5204-5208; Alexandrov, D.V., Nizovtseva, I.G., Malygin, A.P., Unidirectional Solidification of Binary Melts from a Cooled Boundary: Analytical Solutions of a Nonlinear Diffusion-Limited Problem (2008) J. Phys. Condensed Matter, 20, p. 114105; Aseev, D.L., Alexandrov, D.V., Unidirectional Solidification with a Mushy Layer. The Influence of Weak Convection (2006) Acta Materialia, 54, pp. 2401-2406; Aseev, D.L., Alexandrov, D.V., Directional Solidification of Binary Melts with a Non-Equilibrium Mushy Layer (2006) Int. J. Heat Mass Transfer, 49, pp. 4903-4909; Batchelor, G.K., Transport Properties of Two-Phase Materials with Random Structure (1974) Ann. Rev. Fluid Mech., 6, pp. 227-255; Buyevich, Y.A., Alexandrov, D.V., (2005) Heat Transfer in Dispersions, , New York: Begell House; Buyevich, Y.A., Alexandrov, D.V., Mansurov, V.V., (2001) Macrokinetics of Crystallization, , New York: Begell House; Eicken, H., Structure of Under-Ice Melt Ponds in the Central Arctic and Their Effect on the Sea-Ice Cover (1994) Limnol. Oceanogr., 39 (3), pp. 682-694; Eicken, H., Krouse, H.R., Kadko, D., Perovich, D.K., Tracer Studies of Pathways and Rates of Meltwater Transport through Arctic Summer Sea Ice (2002) J. Geophys. Res., 107 (C10), pp. 1-20; Flemings, M.C., (1974) Solidification Processing, , New York: McGrow-Hill Book Company; Fowler, A.C., The Formation of Freckles in Binary Alloys (1985) IMA J. Appl. Maths., 35, pp. 159-174; Gradinger, R., Occurrence of an Algal Bloom Under Arctic Pack Ice (1996) Mar. Ecol.: Proc. Ser., 131, pp. 301-305; Hanson, A.N., Studies of the Mass Budget of Arctic Pack-Ice Floes (1965) J. Glaciol., 5, pp. 701-709; Hills, R.N., Loper, D.E., Roberts, P.H., A Thermodynamically Consistent Model of a Mushy Zone (1983) Q. J. Appl. Math., 36, pp. 505-539; Huppert, H.E., Worster, M.G., Dynamic Solidification of a Binary Melt (1985) Nature, 314, pp. 703-707; Jeffries, M.O., Schwartz, K., Morris, K., Evidence for Platelet Ice Accretion in Arctic Sea Ice Development (1995) J. Geophys. Res., 100 (C6), pp. 10905-10914; Kerr, R.C., Woods, A.W., Worster, M.G., Huppert, H.E., Solidification of An Alloy Cooled from Above. Part 1. Equilibrium Growth (1990) J. Fluid Mech., 216, pp. 323-342; Martin, S., Kauffman, P., The Evolution of Under-Ice Melt Ponds, or Double Diffusion at the Freezing Point (1974) J. Fluid Mech., 64 (3), pp. 507-527; McPhee, M.G., (1986) The Geophysics of Sea Ice, pp. 133-141. , N. Untersteiner (Ed.), New York: Plenum; McPhee, M.G., Maykut, G.A., Morison, J.H., Dynamics and Thermodynamics of the Ice/Upper Ocean System in the Marginal Ice Zone of the Greenland Sea (1987) J. Geophys. Res., 92 (C7), pp. 7017-7031; Morison, J., McPhee, M., Muench, R., The LeadEx Group. The LeadEx Experiment (1993) Eos. Trans. AGU, 74, pp. 393-397; Nansen, F., (1897) Farthest North, p. 235. , New York: Harper Brothers; Notz, D., McPhee, M.G., Worster, M.G., Impact of Underwater-Ice Evolution on Arctic Summer Sea Ice (2003) J. Geophys. Res., 108 (C7), p. 3223; Owen, P.R., Thomson, W.R., Heat Transfer across Rough Surfaces (1963) J. Fluid Mech., 15, pp. 321-334; Peixoto, J.P., Oort, A.M., (1992) Physics of Climate, , New York: American Institute of Physics; Perovich, D.K., Maykut, G.A., Solar Heating of a Stratified Ocean in the Presence of a Static Ice Cover (1990) J. Geophys. Res., 95 (C10), pp. 18233-18245; Perovich, D.K., Andreas, E.L., Curry, J.A., Year on Ice Gives Climate Insights (1999) EOS Trans. AGU, 80, p. 481; Pritchard, R.S., (1980) Sea Ice Processes and Models, , Seattle: Wash.: Univ. of Wash. Press; Scheil, E., Bemerkungen zur Schichtkiistallbildung (1942) Zeichrift Fur Metallkunde, 34, pp. 70-72; Stefan, J., Uber Einige Probleme der Theorie der Warmeleitung (1889) Sitzungsberichte De Mathematisch-Naturawissenschaftlichen Classe Der Kaiserlichen, Akademie Der Wissenschaften, 98 (2 a), pp. 473-484; Stefan, J., Uber die Theorie der Eisbildung, Insbesondere uber die Eisbildung im Polarmeere (1889) Sitzungsberichte De Mathematisch-Naturawissenschaftlichen Classe Der Kaiserlichen, Akademie Der Wissenschaften, 98 (2 a), pp. 965-983; Unterstainer, N., Badgley, F.I., (1958) Preliminary Results of Thermal Budget Studies on Arctic Pack Ice during Summer and Autumn. Arctic Sea Ice, pp. 85-92. , Washington, DC: Nat. Acad. Sci., Nat. Res. Counc. Publ; Wadhams, P., The Underside of Arctic Sea Ice Imaged by Sidescan Sonar (1988) Nature, 333, pp. 161-164; Wadhams, P., Martin, S., Processes Determining the Bottom Topography of Multiyear Arctic Sea Ice (1990) Sea Ice Properties and Processes, pp. 136-141. , W. F. Weeks and S. F. Ackley (Eds.), Hanover: Cold Regions Res. and Eng. Lab; Wettlaufer, J.S., Worster, M.G., Huppert, H.E., Solidification of Leads: Theory, Experiment, and Field Observations (2000) J. Geophys. Res., 105 (C1), pp. 1123-1134; Worster, M.G., Solidification of an Alloy from a Cooled Boundary (1986) J. Fluid Mech., 167, pp. 481-501; Yaglom, A.M., Kader, B.A., Heat and Mass Transfer between a Rough Wall and Turbulent Flow at High Reynolds and Peclet Numbers (1974) J. Fluid Mech., 62, pp. 601-623
Correspondence Address Alexandrov, D. V.; Gor'ky Urals State University, Yekaterinburg, Russian Federation; email: Dmitri.Alexandrov@usu.ru
Language of Original Document English
Abbreviated Source Title Oceanology
Source Scopus