Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-19T15:15:27.251Z Has data issue: false hasContentIssue false
  • English
  • Français

On heating a stable salinity gradient from below

Published online by Cambridge University Press:  19 April 2006

Herbert E. Huppert  and
P. F. Linden
Herbert E. Huppert
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
P. F. Linden
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

When heat is applied at the bottom of a stable salinity gradient a series of layers with uniform temperature and salinity is formed. The evolution of this system is investigated in the laboratory and a numerical model of the process is developed. New layers are formed sequentially at the top of a growing convection region while lower down adjacent layers merge. For given fluid properties the convection depends upon one parameter Q, which is proportional to the (suitably non-dimensionalized) ratio of the salinity gradient to the heat flux. We find that the depth of the top of the convecting region and the number of layers present increase like the square root of time over the range of Q examined. This permits the definition of an effective conductivity, KT, for the total series of layers which is directly proportional to κT, the molecular thermal diffusivity, and inversely proportional to Q. The vertical growth of the layers is thus retarded by increasing Q. The average thickness of the layers decreases with increasing salinity gradient and appears to be independent of the applied heat flux.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 95 , Issue 3 , 11 December 1979 , pp. 431 - 464
Copyright
© 1979 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Chen, C. F., Briggs, D. G. & Wirtz, R. A. 1971 Stability of thermal convection in a salinity gradient due to lateral heating. Int. J. Heat Mass Transfer 14, 57–65.Google Scholar
Crapper, P. F. 1975 Measurements across a diffusive interface. Deep-Sea Res. 22, 537–545.Google Scholar
Degens, E. T. & Ross, D. A. 1969 Hot Brines and Recent Heavy Metal Deposits in the Red Sea. Springer.
Huppert, H. E. 1971 On the stability of a series of double-diffusive layers. Deep-Sea Res. 18, 1005–1021.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. Oceanog. 2, 456–461.Google Scholar
Linden, P. F. 1974 A note on the transport across a diffusive interface. Deep-Sea Res. 21, 283–287.Google Scholar
Linden, P. F. 1975 The deepening of a mixed layer in a stratified fluid. J. Fluid Mech. 71, 385–405.Google Scholar
Linden, P. F. 1976 The formation and destruction of fine-structure by double-diffusive processes. Deep-Sea Res. 23, 895–908.Google Scholar
Marmorino, G. O. & Caldwell, D. R. 1976 Heat and salt transport through a diffusive thermohaline interface. Deep-Sea Res. 23, 59–67.Google Scholar
Neal, V. T., Neshyba, S. & Denner, W. 1969 Thermal stratification in the Arctic Ocean. Science 166, 373–374.Google Scholar
Newman, F. C. 1976 Temperature steps in Lake Kivu: A bottom heated saline lake. J. Phys. Oceanog. 6, 157–163.Google Scholar
Oster, G. 1965 Density gradients. Scientific American 213, 70–76.Google Scholar
Smith, G. D. 1965 Numerical Solution of Partial Differential Equations. Oxford University Press.
Turner, J. S. 1965 The coupled turbulent transports of salt and heat across a sharp density interface. Int. J. Heat Mass Transfer 8, 759–767.Google Scholar
Turner, J. S. 1968 The behaviour of a stable salinity gradient heated from below. J. Fluid Mech. 33, 183–200.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
Turner, J. S. & Stommel, H. 1964 A new case of convection in the presence of combined vertical salinity and temperature gradients. Proc. Natl Acad. Sci. 52, 49–53.Google Scholar