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The diffusive interface in double-diffusive convection

Published online by Cambridge University Press:  12 April 2006

P. F. Linden  and
T. G. L. Shirtcliffe
P. F. Linden
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
T. G. L. Shirtcliffe
Affiliation:
Physics Department, Victoria University of Wellington, New Zealand
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Abstract

A model of the diffusive interface in double-diffusive convection at high Rayleigh number is proposed. The interface is assumed to have a double structure: two marginally stable boundary layers from which blobs or thermals arise on the outer edges of the interface, separated by a diffusive core across which all transport takes place by molecular diffusion. The model is time-independent and comparison is made with unsteady ‘run-down’ experiments on the assumption that the experiments run down through a sequence of equilibrium states each of which can be considered separately. The model predicts a constant ratio of the buoyancy fluxes of the two components at a value equal to the square root of the ratio of their molecular diffusivities, and individual fluxes in reasonable agreement with the available experimental data. Some time-dependent features of the model are also examined.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 87 , Issue 3 , 15 August 1978 , pp. 417 - 432
Copyright
© 1978 Cambridge University Press

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References

Baines, P. G. & Gill, A. E. 1969 On thermohaline convection with linear gradients. J. Fluid Mech. 37, 289–306.Google Scholar
Busse, F. H. & Whitehead, J. A. 1974 Oscillatory and collective instabilities in large Prandtl number convection. J. Fluid Mech. 66, 67–80.Google Scholar
Crapper, P. F. 1975 Measurements across a diffusive interface. Deep-Sea Res. 22, 537–545.Google Scholar
Crapper, P. F. & Linden, P. F. 1974 The structure of turbulent density interfaces. J. Fluid Mech. 65, 45–63.Google Scholar
Foster, T. D. 1971 Intermittent convection. Geophys. Fluid Dyn. 2, 201–217.Google Scholar
Howard, L. N. 1964 Convection at high Rayleigh number. Proc. 11th Int. Cong. Appl. Mech., pp. 1109–1115. Springer.
Huppert, H. E. & Moore, D. R. 1976 Nonlinear double-diffusive convection. J. Fluid Mech. 78, 821–854.Google Scholar
Linden, P. F. 1973 On the structure of salt fingers. Deep-Sea Res. 20, 325–340.Google Scholar
Linden, P. F. 1974 A note on the transport across a diffusive interface. Deep-Sea Res. 21, 283–287.Google Scholar
Marmorino, G. O. & Caldwell, D. R. 1976 Equilibrium heat and salt transport through a diffusive thermohaline interface. Deep-Sea Res. 23, 59–68.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, 27–43.Google Scholar
Sparrow, E., Husar, R. B. & Goldstein, R. J. 1970 Observations and other characteristics of thermals. J. Fluid Mech. 41, 793–800.Google Scholar
Straus, J. M. 1972 Finite amplitude doubly diffusive convection. J. Fluid Mech. 56, 353–374.Google Scholar
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. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
Turner, J. S. 1974 Double-diffusive phenomena. Ann. Rev. Fluid Mech. 6, 37–56.Google Scholar
Veronis, G. 1965 On finite amplitude instability in thermohaline convection. J. Mar. Res. 23, 1–17.Google Scholar
Veronis, G. 1968 Effect of a stabilizing gradient of solute on thermal convection. J. Fluid Mech. 34, 315–336.Google Scholar