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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
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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

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