An influence of the false bottom on the nonlinear dynamics of the water freezing process

I. G. Nizovtseva ; D. V. Alexandrov

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2011), pp. 89-99.

Résumé

The current paper casts the light on the processes of structural-phase transitions during the freezing salt water, including the false bottom effects. A nonlinear mathematical model of heat and mass transfer was obtained. It takes into account the presence of three moving boundaries of phase transition and turbulent fluid flows from the ocean side by the surface of the false bottom. The exact analytical solutions of the nonlinear model were obtained — in their turn, they takes into account the time dependence of temperature and salinity at the depth and fluctuations of friction velocity. The distribution of temperature and salinity, the concentration of solids, the laws of motion of the boundaries of the phase transition, “salt water — the two-phase zone”, “two-phase zone — melted water” and “melt-water — ice” were found. The heat flux at the lower boundary of a false bottom was specified. The latter can change its direction at the time oscillations of the sea water temperature and friction velocity. Also it was shown, that structural transitions in the ice thickness are strictly associated with the processes of evolution of a false bottom.

Détail

Keywords: crystallization, heat and mass transfer, Stefan problem, two-phase zone, false bottom.

Bibliographie

[1] Martin S., Kauffman P., “The evolution of under-ice melt ponds, or double diffusion at the freezing point”, J. Fluid Mech., 64:3 (1974), 507–528 | DOI

[2] Unterstainer N., “Natural desalination and equilibrium salinity profile of old sea ice”, Physics of snow and ice, v. 1, ed. H. Oura, Hokkaido University, 1967, 569–577

[3] Hanson A. M., “Studies of the mass budget of Arctic pack-ice floes”, J. Glaciology, 5:41 (1965), 701–709

[4] Nansen F., Farthest North, Harper Brothers, New York, 1897

[5] Zubov N. N., Artic ice, U.S. Navy Electronics Laboratory, San Diego, Calif., 1963, 491 pp.

[6] Unterstainer N., Badgley F. I., “Preliminary results of thermal budget studies on Arctic pack ice during summer and autumn”, Arctic sea ice, Nat. Acad. Sci., Nat. Res. Counc, Washington, 1958, 85–92

[7] Eicken H., “Structure of under-ice melt ponds in the central Arctic and their effect on, the sea-ice cover”, Limnol. Oceanogr., 39:3 (1994), 682–694 | DOI

[8] Notz D., McPhee M. G., Worster M. G., Maykut G. A., Schlünzen, K. H., Eicken H., “Impact of underwater-ice evolution on Arctic summer sea ice”, J. Geophys. Res., 108:C7 (2003), 3223, 12 pp. | DOI

[9] Jeffries M. O., Schwartz K., Morris K., Veazey A. D., Krouse H. R., Cushing S., “Evidence for platelet ice accretion in Arctic sea ice development”, J. Geophys. Res, 100:C6 (1995), 10,905–10,914 | DOI

[10] Wadhams P., “The underside of Arctic sea ice imaged by sidescan sonar”, Nature, 333 (1988), 161–164 | DOI

[11] Wadhams P., Martin S., “Processes determining the bottom topography of multiyear Arctic sea ice”, Sea ice properties and processes, eds. W. F. Weeks, S. F. Ackley, Hanover, 1990, 136–141

[12] Eicken H., Krouse H. R., Kadko D., Perovich D. K., “Tracer studies of pathways and rates of meltwater transport through Arctic summer sea ice”, J. Geophys. Res., 107:C10 (2002), 8046, 20 pp. | DOI

[13] Perovich D. K. et al., “Year on Ice Gives Climate Insights”, EOS Trans. AGU, 80:41 (1999), 481, 485–486 | DOI

[14] Gradinger R., “Occurrence of an algal bloom under Arctic pack ice”, MEPS, 131 (1996), 301–305 | DOI

[15] Hills R. N., Loper D. E., Roberts P. H., “A thermodynamically consistent model of a mushy zone”, Q. J. Mech. Appl. Math., 36:4 (1983), 505–540 | DOI

[16] Buyevich Yu. A., Alexandrov D. V., Mansurov V. V., Macrokinetics of crystallization, Begell House Inc., New York – Wallingford, 2001, 183 pp.

[17] Alexandrov D. V., Malygin A. P., Alexandrova I. V., “Solidification of leads: approximate solutions of non-linear problem”, Ann. Glaciol, 44:1 (2006), 118–122 | DOI | MR

[18] 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”, Doklady Earth Sciences, 411:2 (2006), 1407–1411 | DOI

[19] Scheil E., “Bemerkungen zur schichtkiistallbildung”, Zeitschrift für Metallkunde, 34 (1942), 70–72

[20] McPhee M. G., “The upper Ocean”, The Geophysics of Sea Ice, NATO ASI series. Series B, Physics, 146, ed. N. Untersteiner, Plenum Press, New York, 1986, 133–141

[21] 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”, J. Geophys. Res., 92:C7 (1987), 7017–7031 | DOI

[22] Yaglom A. M., Kader B. A., “Heat and mass transfer between a rough wall and turbulent fluid flow at high Reynolds and Péclet numbers”, J. Fluid Mech., 62:3 (1974), 601–623 | DOI | Zbl

[23] Alexandrov D. V., Aseev D. L., Nizovtseva I. G., Huang H.-N., Lee D., “Nonlinear dynamics of directional solidification with a mushy layer. Analytic solutions of the problem”, Int. J. Heat Mass Transfer, 50:17–18 (2007), 3616–3623 | DOI | Zbl

[24] Aleksandrov D. V., Nizovtseva I. G., “Nonlinear dynamics of the false bottom during seawater freezing”, Dokl. Earth Sci., 419:2 (2008), 359–362 | DOI | Zbl

[25] Alexandrov D. V., Nizovtseva I. G., “To the theory of underwater ice evolution, or nonlinear dynamics of “false bottoms””, Int. J. Heat Mass Transfer, 51:21–22 (2008), 5204–5208 | DOI | Zbl