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Buoyancy transfer across a diffusive interface

Published online by Cambridge University Press:  26 April 2006

Harindra J. S. Fernando
Harindra J. S. Fernando
Affiliation:
Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106, USA
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Abstract

An experimental investigation of various aspects of buoyancy transfer across a diffusive density interface that separates stably stratified, turbulently convecting layers of relatively fresh cold water overlying hot salty water is described. It is argued that the interfacial layer should possess a double boundary-layer structure, in which the thicknesses of the salt and heat interfacial layers are determined by a balance between the opposing effects of diffusion and entrainment. Based on this argument, a simple theory, that predicts the interfacial-layer thickness, the diffusive heat and salt fluxes across the density interface, and the time variation of the temperature and salt concentrations in the convecting layers, is proposed for the case in which the convection is driven by a constant heat flux supplied to the lower layer. During a certain time interval, the theory and experiment agree well, but thereafter distinct differences can be seen. Measurements suggest that these differences may be due to the distortion of the density interface at low interfacial stabilities by turbulent eddies, which leads to a change in the buoyancy transfer mechanism. When the Richardson number falls below a critical value Riv, the interface was found to migrate slowly upwards and the mechanism of entrainment was the detachment of thin sheets of fluid by eddies scouring the interface.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 209 , December 1989 , pp. 1 - 34
Copyright
© 1989 Cambridge University Press

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References

Adrian, R. J., Ferreira, R. T. D. & Boberg, T. 1986 Turbulent convection in wide horizontal layers. Expts Fluids 4, 121.Google Scholar
Crapper, P. F. 1975 Measurements across a diffusive interface. Deep-Sea Res. 22, 537.Google Scholar
Crapper, P. F. & Linden, P. F. 1974 The structure of the turbulent density interacs. J. Fluid Mech. 65, 45.Google Scholar
Degens, E. T. & Ross, D. A. 1969 Hot Brines and Recent Heavy Metal Deposits in the Red Sea. Springer.
Fernando, H. J. S. 1989 Oceanographic implications of laboratory experiments on diffusive interfaces. J. Phys. Oceanogr. (in Press.)Google Scholar
Fernando, H. J. S. & Long, R. R. 1983 The growth of a grid-generated turbulent mixed layer in a two-fluid system. J. Fluid Mech. 133, 377.Google Scholar
Fernando, H. J. S. & Long, R. R. 1985 On the nature of the entrainment interface of a two-layer fluid subjected to zero-mean-shear turbulence. J. Fluid Mech. 151, 21.Google Scholar
Foster, T. D. & Carmack, E. C. 1976 Temperature and salinity structure in the Weddell Sea. J. Phys. Oceanogr. 6, 36.Google Scholar
Gregg, M. S. & Cox, C. S. 1972 The vertical microstructure of temperature and salinity. Deep-Sea Res. 19, 355.Google Scholar
Griffiths, R. W. 1979 The transport of multiple components through thermohaline diffusive interfaces. Deep-Sea Res. 26, 383.Google Scholar
Hannoun, I. A., Fernando, H. J. S. & List, E. J. 1988 Turbulence structure near a sharp density interface. J. Fluid Mech. 189, 189.Google Scholar
Hannoun, I. A. & List, E. J. 1988 Turbulent mixing at a shear-free density interface. J. Fluid Mech. 189, 211.Google Scholar
Hendricks, P. J., Muench, R. D. & Stegan, G. R. 1985 A heat balance for the Bering Sea Ice Edge. J. Phys. Oceanogr. 15, 1747.Google Scholar
Hoare, R. A. 1966 Problems of heat transfer in Lake Vanda, a density stratified Arctic lake. Nature 210, 787.Google Scholar
Hoare, R. A. 1968 Thermohaline convection in Lake Vanda, Antarctica. J. Geophys. Res. 73, 607.Google Scholar
Hunt, J. C. R. 1983 Turbulence structure and turbulent diffusion near gas—liquid interface. In Proc. Intl Symp. on Gas Transfer across Water Surfaces, Ithaca, N.Y. (ed. W. Brutsaert & G. H. Jirka).
Hunt, J. C. R. 1984 Turbulence structure in thermal convection and shear-free boundary layers. J. Fluid Mech. 138, 161.Google Scholar
Huppert, H. E. 1971 On the stability of a series of double diffusive layers. Deep-Sea Res. 18, 1005.Google Scholar
Huppert, H. E. & Turner, J. S. 1972 Double diffusive convection and its implications for the temperature and salinity structure of the ocean and Lake Vanda. J. Phys. Oceanogr. 2, 456.Google Scholar
Huppert, H. E. & Turner, J. S. 1981 Double-diffusive convection. J. Fluid Mech. 106, 299.Google Scholar
Kantha, L. H. 1986 Comments on ‘A heat balance for the Bering Sea Ice Edge’. J. Phys. Oceanogr. 16, 2205.Google Scholar
Linden, P. F. 1974 A note on the transport across a diffusive interface. Deep-Sea Res. 21, 283.Google Scholar
Linden, P. F. & Shirtcliffe, T. G. L. 1978 The diffusive interface in double-diffusive convection. J. Fluid Mech. 87, 417 (referred to as LS).Google Scholar
Long, R. R. 1978 A theory of mixing in stably stratified fluids. J. Fluid Mech. 84, 113.Google Scholar
Marmorino, G. O. & Caldwell, D. R. 1976 Heat and salt transport through a diffusive thermohaline interface. Deep-Sea Res. 23, 59.Google Scholar
Munns, R. G., Stanley, R. J. & Densmore, C. D. 1967 Hydrographic observations of the Red Sea brines. Nature 214, 1215.Google Scholar
Narusawa, V. 1986 Structure of diffusive interface of double diffusive convection. ASME paper 86-HT-3.Google Scholar
Neal, V. T., Neshyba, S. & Denner, W. 1969 Thermal stratification in the Arctic Ocean. Science 166, 373.Google Scholar
Neshyba, S., Neal, V. T. & Denner, W. 1971 Temperature and conductivity measurements under Ice Island T-3. J. Geophys. Res. 76, 8107.Google Scholar
Newell, T. A. 1984 Characteristics of double-diffusive interface at high density-stability ratios. J. Fluid Mech. 149, 385.Google Scholar
Newman, F. C. 1976 Temperture steps in Lake Kivu: a bottom heated saline lake. J. Phys. Oceanogr. 6, 157.Google Scholar
Pearson, H. & Linden, P. F. 1983 The final state of decay of turbulence in stably stratified fluid. J. Fluid Mech. 134, 195.Google Scholar
Shirtcliffe, T. G. L. 1973 Transport and profile measurements of the diffusive interface in double diffusive convection with similar diffusivities. J. Fluid Mech. 57, 27.Google Scholar
Shirtcliffe, T. G. L. & Calhaem, I. M. 1968 Measurements of temperature and electrical conductivity in Lake Vanda, Victoria Land, Antarctica. N. Z. J. Geol. Geophys. 11, 976.Google Scholar
Sparrow, E. M., Husar, R. B. & Goldstein, R. J. 1970 Observations and other characteristics of thermals. J. Fluid Mech. 41, 793.Google Scholar
Stegan, G. R., Hendricks, P. J. & Muench, R. D. 1985 Vertical Mixing on the Bering Sea shelf. In The Ocean Surface Wave Breaking, Turbulent Mixing and Radio Probing (ed. Y. Toba & H. Mitsuyasu), p. 547. Reidel.
Stern, M. E. 1982 Inequalities and variational principles in double diffusive turbulence. J. Fluid Mech. 114, 105.Google Scholar
Swallow, J. C. & Crease, J. 1965 Hot salty water at the bottom of the Red Sea. Nature 205, 165.Google Scholar
Takao, S. & Narusawa, V. 1980 An experimental study of heat and mass transfer across a diffusive interface. Intl J. Heat Mass Transfer 23, 1283.Google Scholar
Taylor, J. 1988 The fluxes across a diffusive interface at low values of the density ratios. Deep-Sea Res. 35, 555.Google Scholar
Turner, J. S. 1965 The coupled turbulent transports of salt and heat across a sharp density interface. Intl J. Heat Mass Transfer 8, 759.Google Scholar
Turner, J. S. 1968 The behaviour of a salinity gradient heated from below. J. Fluid Mech. 33, 183.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
Turner, J. S. 1974 Double diffusive phenomena. Ann. Rev. Fluid Mech. 6, 37.Google Scholar
Turner, J. S. 1985 Multicomponent convection. Ann. Rev. Fluid Mech. 17, 11.Google Scholar
Turner, J. S., Shirtcliffe, T. G. L. & Brewer, P. G. 1970 Elemental variations of transport coefficients across density interfaces in multiple-diffusive systems. Nature 228, 1083.Google Scholar
Turner, J. S. & Stommel, H. 1964 A new case of convection in the prsence of combined vertical salinity and temperature gradients. Proc. Natl. Acad. Sci. 52, 49.Google Scholar
Veronis, G. 1968 Effect of stabilizing gradient of solute on thermal convection. J. Fluid Mech. 34, 315.Google Scholar