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Ice stalactites: comparison of a laminar flow theory with experiment

  • Seelye Martin (a1)
Abstract

Recent field observations in the polar oceans show that the hollow tubes of ice called ice stalactites form around streamers of cold brine rejected by the growing sea ice. In a laboratory study of this process, we inject cold, dense brine a t a constant salinity, temperature and volume flux into an insulated tank of sea water held at its freezing point, then photograph the resultant stalactite growth. Because the inner wall temperature of the stalactite remains on the salinity-determined freezing curve, as the stalactite grows and the temperature deficit of the brine goes into the growth of ice, the inner wall melts to dilute and cool the adjacent brine back to its freezing point. This melting means that both the inner and outer stalactite radii increase with time. The radius of the stalactite tip, which is constant for each experiment, is shown to be controlled by the onset of a convective instability. If the tip becomes too large, overturning occurs and the sea-water intrusion freezes, reducing the radius of the tip so that the flow leaving the tip is marginally stable. Inside the stalactite, since the inner radius increases with time, both theory and experiment show the interior flow to be convectively unstable. The present study also derives a solution from the constant-heat-flux Graetz solution for the growth in both length and side-wall area of the stalactite. The experiments show that away from the stalactite base and the very beginning of the experiment this solution, with convection accounted for by an adjustable coefficient, describes the experimental growth. Finally, analysis of the experiments shows that as much as 50% of the ice represented by the cold brine does not go into the stalactite, rather the ice goes directly into the ocean as loose crystals.

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Barer, D. J. 1966 A technique for the precise measurement of small fluid velocities. J. Fluid Mech. 26, 573.
Carslaw, H. S. & Jaeger, J. C. 1959 Conduction of Heat in Solids. Oxford University Press.
Dayton, P. K. & Martin, S. 1971 Observations of ice stalactites in McMurdo Sound, Antarctica. J. Geophys. Res. 76, 1595.
Eide, L. I. & Martin, S. 1974 The formation of brine drainage features in young sea ice. Submitted to J. Glaciol.
Ellison, T. H. & Turner, J. S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 6, 423.
Frank, F. C. 1950 Radially symmetric phase growth controlled by diffusion. Proc. Roy. Soc. A 201, 586.
Goldstein, S. 1938 Modern Developments in Fluid Mechanics, vol. 2. Dover.
Hallman, T. M. 1958 Combined free and forced convection in a vertical tube. Ph.D. thesis, Purdue University (University Microfilms, L.C. Card no. Mic 58-3160, Ann Arbor, Michigan).
Kaufman, D. W. 1960 Sodium Chloride. Reinhold.
Kays, W. M. 1966 Convective Heat and Mass Transport. McGraw-Hill.
Lake, R. A. & Lewis, E. L. 1970 Salt rejection by sea ice during growth. J. Geophys. Res. 75, 583.
Lewis, E. L. & Weeks, W. F. 1971 Sea ice: some polar contrasts. In Symp. om Antarctic Ice & Water Masses (ed. G. Deacon), pp. 2838. Scott Polar Research Institute, University of Cambridge.
Ono, N. 1967 Specific heat and heat of fusion of sea ice. In Physics of Snow and Ice, vol. 1 (ed. H. Oura), pp. 589610. Institute of Low Temperature Science, Hokkaido University, Japan.
Paice, R. A. 1970 Stalactite growth beneath sea ice. Science, 167, 171.
Rouse, H. 1961 Fluid Mechanics for Hydraulic Engineers. Dover.
Scheele, G. F. & Ratty, T. J. 1963 Effect of natural convection instabilities on rates of heat transfer at low Reynolds number. A.I.Ch.E. J. 9, 183.
Scheele, G. F., Rosen, E. M. & Hanratty, T. J. 1960 Effect of natural convection on transition to turbulence in vertical pipes. Can. J. Chem. Eng. 38, 67.
Schlichting, H. 1962 Boundary Layer Theory. McGraw-Hill.
Schwerdtfeger, P. 1963 The thermal properties of sea ice. J. Glaciol. 4, 789.
Weeks, W. F. 1968 Understanding the variations of the physical properties of sea ice. In Symp. on Antarctic Oceanography (ed. R. Currie), pp. 173191. Scott Polar Research Institute, University of Cambridge.
Weeks, W. F. & Lofgren, G. 1967 The effective solute distribution coefficient during the freezing of NaCl solutions. In Physics of Xnow and Ice, vol. 1 (ed. H. Oura), pp. 579599. Institute of Low Temperature Science, Hokkaido University, Japan.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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