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Heat thermal structure in the interfacial boundary layer measured in an open tank of water in turbulent free convection

Published online by Cambridge University Press:  12 April 2006

Kristina B. Katsaros ,
W. Timothy Liu ,
Joost A. Businger  and
James E. Tillman
Kristina B. Katsaros
Affiliation:
Department of Atmospheric Sciences, University of Washington, Seattle
W. Timothy Liu
Affiliation:
Department of Atmospheric Sciences, University of Washington, Seattle
Joost A. Businger
Affiliation:
Department of Atmospheric Sciences, University of Washington, Seattle
James E. Tillman
Affiliation:
Department of Atmospheric Sciences, University of Washington, Seattle
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Abstract

The thermal structure in the boundary layer and its relation to the heat flux from the cooling and evaporating surface of a deep tank of water are investigated. When a deep layer of water in contact with still air above loses heat to the air, the cooled water in a region just under the surface converges along lines and then plunges down in sheets. These sheets of falling water dissipate as they move into the body of the water, which is in turbulent motion. The vertical profiles of the horizontally averaged temperature and its standard deviation agree fairly closely with theoretical profiles based on time averages of the solution to the heat diffusion equation. The differences between observed and thus predicted profile shapes are consistent with the expected effects of the falling cold thermals and the warm return flow, which are neglected in the theories. The profiles of the standard deviation have large values up to the interface and lie between predictions based on boundary conditions of constant surface temperature and constant heat flux, in keeping with the experimental conditions.

The relation between the net heat flux and the temperature difference across the boundary layer is given in non-dimensional form by N = 0[sdot ]156R0[sdot ]33, which is in good agreement with the asymptotic similarity prediction N [vprop ] R1/3 but lower than theoretical calculations of the upper bound of N vs. R.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 83 , Issue 2 , 22 November 1977 , pp. 311 - 335
Copyright
© 1977 Cambridge University Press

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References

Ball, F. K. 1954 Austr. J. Phys. 7, 649.
Bénard, H. 1901 Ann. Chim. Phys. 11, 1261.
Berg, J. C., Acrivos, A. & Boudart, M. 1966 Adv. Chem. Engng 6, 61.
Berg, J. C. & Mong, C. R. 1969 Density effect in interfacial convection. Chem. Engng Sci. 24, 937–946.Google Scholar
Businger, J. A. 1973 Boundary-Layer Met. 4, 323.
Busse, F. H. 1969 J. Fluid Mech. 37, 457.
Carroll, J. J. 1971 The structure of turbulent convection. Ph.D. thesis, Dept. of Meteorology, University of California, Los Angeles.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford: Clarendon Press.
Chang, J. H. & Wagner, R. N. 1975 J. Geophys. Res. 80, 2677.
Chu, T. Y. & Goldstein, R. J. 1973 J. Fluid Mech. 60, 141.
Danckwerts, P. V. 1951 Ind. Engng Chem. 43, 1460.
Deardorff, J. W. & Willis, G. E. 1967a J. Fluid Mech. 28, 675.
Deardorff, J. W. & Willis, G. E. 1967b Quart. J. Roy. Met. Soc. 93, 166.
Elder, J. W. 1969 J. Fluid Mech. 35, 417.
Ewing, G. & McAlister, E. D. 1960 Science 13, 1374.
Fitzjarrald, D. E. 1976 J. Fluid Mech. 73, 693.
Foster, T. D. 1965 Phys. Fluids 8, 1770.
Foster, T. D. 1971 Geophys. Fluid Dyn. 2, 201.
Globe, S. & Dropkin, D. 1959 J. Heat Transfer 81, 24.
Goldstein, R. J. & Chu, T. Y. 1969 Prog. Heat Mass Transfer 2, 55.
Gough, D. O., Spiegel, E. A. & Toomre, J. 1975 J. Fluid Mech. 68, 695.
Hasse, L. 1963 Tellus 15, 363.
Häussler, W. 1956 Wiss. Z. Tech. Hochschule Dresden 5, 435.
Herring, J. R. 1963 J. Atmos. Sci. 20, 325.
Herring, J. R. 1964 J. Atmos. Sci. 21, 277.
Higbie, R. 1935 Trans. A.I.Ch.E. 31, 365.
Howard, L. N. 1963 J. Fluid Mech. 17, 405.
Howard, L. N. 1966 Proc. 11th Int. Cong. Appl. Mech., Munich, 1964 (ed. H. Görtler), p. 1109.
Jeffreys, H. 1926 Phil. Mag. 2, 833.
Jeffreys, H. 1928 Proc. Roy. Soc. 118, 195.
Kanwischer, J. 1963 Deep-Sea Res. 10, 195.
Katsaros, K. B. 1973 J. Phys. Ocean. 3, 482.
Katsaros, K. B. 1975 Turbulent free convection in fresh and salt water, some characteristics revealed by visualization. Rep. Dept. Atmos. Sci., Univ. Wash.Google Scholar
Katsaros, K. B. & Businger, J. A. 1973 J. Geophys. Res. 78, 1964.
Katsaros, K. B. & Liu, W. T. 1974 J. Phys. Ocean. 4, 654.
Kraichnan, R. H. 1962 Phys. Fluids 5, 1374.
Krishnamurti, R. 1970 J. Fluid Mech. 42, 309.
Krishnamurti, R. 1973 J. Fluid Mech. 60, 285.
Liu, W. T. 1974 Thermal structure and heat transport in the molecular boundary layer under an evaporating surface of a deep tank of water. M.S. thesis, Dept. of Atmospheric Sciences, University of Washington, Seattle.
Liu, W. T. & Businger, J. A. 1975 Geophys. Res. Lett. 2, 403.
Low, A. R. 1929 Proc. Roy. Soc. A 125, 190.
Mcalister, E. D. 1964 Appl. Opt. 3, 609.
Mcalister, E. D. 1967 Ocean Ind. 215, 35.
Mcalister, E. D. 1969 Ocean from Space. Gulf Publishing Co.
Mcalister, E. D. & McLeish, W. 1969 J. Geophys. Res. 74, 3408.
Mcalister, E. D. & McLeish, W. 1970 Appl. Opt. 9, 2697.
Mcalister, E. D., McLeish, W. & Corduan, A. 1971 J. Geophys. Res. 76, 4172.
Malkus, W. V. R. 1954a Proc. Roy. Soc. A 225, 185.
Malkus, W. V. R. 1954b Proc. Roy. Soc. A 225, 196.
Matisse, P. 1974 A flow-indicating fluid. Rep. Kalliroscope Corp., 145 Main Street, Cambridge, Mass.
Moore, D. R. & Weiss, N. O. 1973 J. Fluid Mech. 58, 289.
Mull, W. & Reiher, H. 1930 Beihefte Gesundheitsing Ing. ser. 1, p. 28.
Pearson, J. R. A. 1958 J. Fluid Mech. 4, 489.
Pellew, A. & Southwell, R. V. 1940 Proc. Roy. Soc. A 176, 312.
Ramdas, L. E. & Raman, P. K. 1946 Indian Acad. Sci. Proc. A 23, 127.
Rayleigh, Lord 1916 Phil. Mag. 32, 529.
Roll, H. I. 1965 Physics of the Marine Atmosphere. Academic Press.
Rossby, H. T. 1969 J. Fluid Mech. 36, 309.
Schmidt, G. & Silveston, P. L. 1959 Chem. Engng Prog. Symp. Ser. 29, 55.
Schmidt, R. J. & Milverton, S. W. 1935 Proc. Roy. Soc. A 152, 586.
Schmidt, R. J. & Saunders, O. A. 1938 Proc. Roy. Soc. A 165, 216.
Somerscales, E. F. C. & Gazda, I. W. 1969 J. Heat Mass Transfer 12, 1491.
Spangenberg, W. G. & Rowland, W. R. 1961 Phys. Fluids 4, 743.
Sparrow, E. M., Husar, R. B. & Goldstein, R. J. 1970 J. Fluid Mech. 41, 793.
Straus, J. M. 1973 Geophys. Fluid Dyn. 5, 261.
Straus, J. M. 1976 Dyn. Atmos. Oceans 1, 77.
Thomas, D. B. & Townsend, A. A. 1957 J. Fluid Mech. 2, 473.
Tillman, J. E. 1972 J. Appl. Met. 11, 783.
Townsend, A. A. 1959 J. Fluid Mech. 5, 209.
Veronis, G. 1966 J. Fluid Mech. 26, 49.
Willis, G. E. & Deardorff, J. W. 1965 Phys. Fluids 8, 2225.
Willis, G. E. & Deardorff, J. W. 1967a Phys. Fluids 10, 931.
Willis, G. E. & Deardorff, J. W. 1967b Phys. Fluids 10, 1861.
Woodcock, A. H. 1941 J. Mar. Res. 4, 153.
Woodcock, A. H. & Stommel, H. 1947 J. Met. 4, 102.