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Steady subcritical thermohaline convection

Published online by Cambridge University Press:  20 April 2006

M. R. E. Proctor
M. R. E. Proctor
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

Steady convective motions in a Boussinesq fluid with an unstable thermal and stable salinity stratification are investigated in the case that the ratio of diffusivities τ = κS/κT [Lt ] 1. Using perturbation theory, it is shown that, for any value of the salt Rayleigh number RS, finite-amplitude convection can occur at values of the Ray-leigh number RT much less than that necessary for infinitesimal oscillations, provided only that T is sufficiently small. A simple qualitative argument is used to show how Rmin, the minimum value of RT for steady convection, varies with RS, and it is shown that the analytical results of the present paper form a natural complement to the numerical ones of Huppert & Moore (1976). Results are presented both for stress-free and for rigid boundaries, and applicability of the method to other related problems is suggested.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 105 , April 1981 , pp. 507 - 521
Copyright
© 1981 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. 1975 Nonlinear interaction of magnetic field and convection. J. Fluid Mech. 71, 193–206.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon.
Da Costa, L., Knobloch, E. & Weiss, N. O. 1981 Oscillations in double-diffusive convection. J. Fluid Mech. (to appear).Google Scholar
Huppert, H. E. & Moore, D. R. 1976 Non-linear double diffusive convection. J. Fluid Mech. 78, 821–854.Google Scholar
Malkus, W. V. R. & Veronis, G. 1958 Finite amplitude cellular convection. J. Fluid Mech. 4, 225–260.Google Scholar
Proctor, M. R. E. & Galloway, D. J. 1979 The dynamic effect of flux ropes on Rayleigh-Bénard convection. J. Fluid Mech. 90, 273–287.Google Scholar
Rayleigh, Lord 1916 On convective currents in a horizontal layer of fluid when the higher temperature is on the under side. Phil. Mag. 32 (6), 529–546.Google Scholar
Roberts, G. O. 1979 Fast viscous Bénard convection. Geophys. Astrophys. Fluid Dyn. 12, 235–273.Google Scholar
Shir, C. C. & Joseph, D. D. 1968 Convective instability in a temperature and concentration field. Arch. Rat. Mech. Anal. 30, 38–80.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 stabilising gradient of solute on thermal convection. J. Fluid Mech. 34, 315–336.Google Scholar