Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-21T15:43:57.889Z Has data issue: false hasContentIssue false
  • English
  • Français

Double-diffusive convection with large variable gradients

Published online by Cambridge University Press:  20 April 2006

I. C. Walton
I. C. Walton
Affiliation:
Department of Mathematics, Imperial College, London SW7
Get access Rights & Permissions [Opens in a new window]

Abstract

The onset of double-diffusive convection is discussed for a layer of fluid in which the vertical salinity gradient varies with depth and for which the thermal and saline Rayleigh numbers R and Rs are large. These conditions are similar to those that exist in a solar pond prior to the onset of any instability. It is shown that when convection occurs it takes the form of an overstable mode and is essentially confined to a narrow region of vertical extent $\sim R_{\rm s}^{-\frac{1}{14}} \times $ depth of the fluid layer, centred at the critical depth where the salt gradient is smallest. The leading terms in asymptotic expansions of the ratio R/Rs, the frequency of oscillation p and the horizontal wavenumber a are determined for R, [Gt ] 1. The results predicted by the theory are shown to be in good agreement with numerical results and with observations of solar ponds.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 125 , December 1982 , pp. 123 - 135
Copyright
© 1982 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

Baines, P. G. & Gill, A. E. 1969 On thermohaline convection with linear gradients. J. Fluid Mech. 37, 289–306.Google Scholar
Hauser, S. G. 1976 Exploring stability criteria of solar ponds. A.S.M.E. Publ. 76-WA/HT.62.
Hoare, R. A. 1966 Problems of heat transfer in Lake Vanda. Nature 210, 787.Google Scholar
Huppert, H. E. & Moore, D. R. 1976 Nonlinear double-diffusive convection. J. Fluid Mech. 78, 821–854.Google Scholar
Huppert, H. E. & Turner, J. S. 1981 Double-diffusive convection. J. Fluid Mech. 106, 299–330.Google Scholar
Proctor, M. R. E. 1981 Steady sub-critical thermohaline convection. J. Fluid Mech. 105, 507–521.Google Scholar
Shirtcliffe, T. G. L. 1967 Thermosolutal convection: observation of an overstable mode. Nature 213, 489–490.Google Scholar
Shirtcliffe, T. G. L. 1969 An experimental investigation of thermosolutal convection at marginal stability. J. Fluid Mech. 33, 183–200.Google Scholar
Tabor, H. 1980 Non-convecting solar ponds. Phil. Trans. R. Soc. Lond. A 295, 423–433.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
Walin, G. 1964 Note on the stability of water stratified by both salt and heat. Tellus 16, 389–393.Google Scholar
Weinberger, H. 1964 The physics of the solar pond. Solar Energy 8, 45–56.Google Scholar
Wilson, A. T. & Wellman, H. W. 1962 Lake Vanda: an Antarctic lake. Nature 196, 1171.Google Scholar
Zangrando, F. 1979 Observation and analysis of a full scale experimental salt-gradient solar pond. Ph.D. thesis, Department of Physics and Astronomy, University of New Mexico, New Mexico.