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A theoretical and experimental study of double-layer convection

Published online by Cambridge University Press:  26 April 2006

S. Rasenat ,
F. H. Busse  and
I. Rehberg
S. Rasenat
Affiliation:
Institute of Physics, University of Bayreuth, D-8580 Bayreuth, FRG
F. H. Busse
Affiliation:
Institute of Physics, University of Bayreuth, D-8580 Bayreuth, FRG
I. Rehberg
Affiliation:
Institute of Physics, University of Bayreuth, D-8580 Bayreuth, FRG
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Abstract

The onset of thermal convection in a double layer of two superimposed immiscible fluids heated from below is investigated. The linearized equations of the problem are analysed in a much wider region of the parameter space than has been studied before. It is shown that the onset of steady convection in the two layers may occur in the form of either viscously or thermally coupled motions. In addition to the oscillatory interfacial instability, which depends on a non-vanishing distortion of the interface, there exists another oscillatory instability which corresponds to a cyclic variation between viscous and thermal coupling. Conditions for the onset of this instability are outlined and its connections with the other modes of the system are demonstrated in bifurcation diagrams. In the experiments the shadowgraph method is used for the visualization of the onset of convection and for the measurement of its wavelength. Changeovers between viscous and thermal coupling can be identified, but the experimental realization of an oscillatory onset has been elusive so far.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 199 , February 1989 , pp. 519 - 540
Copyright
© 1989 Cambridge University Press

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References

Busse, F. E.: 1981 On the aspect ratio of two-layer mantle convection. Phys. Earth Planet. Interiors. 24, 320–324.Google Scholar
Busse, F. H.: 1982 Multiple solutions for convection in a two component fluid. Geophys. Res. Lett. 9, 519–522.Google Scholar
Christensen, U. R. & Yuen, D. A., 1984 The interaction of a subducting lithospheric slab with a chemical or phase boundary. J. Geophys. Res. 89, 4389–4402.Google Scholar
Cserepes, L. & Rabinowicz, M., 1985 Gravity and convection in a two-layer-mantle. Earth Planet. Sci. Lett. 76, 193–207.Google Scholar
Cserepes, L., Rabinowicz, M. & Rosemberg-Borot, C. 1988 Three-dimensional convection in a two-layer mantle. J. Geophys. Res. (submitted).Google Scholar
Ellsworth, K. & Schubert, G., 1985 Two-layer convection in the earth mantle, EOS Trans. Am. Geophys. Union 66, 1070.Google Scholar
Frick, H. & Clever, R. M., 1980 Einfluß der Seitenwände auf das Einsetzen der Konvektion in einer horizontalen Flüssigkeitsschicht Z. Angew. Math. Phys. 31, 502–513.
Gershuni, G. Z. & Zhukhovitskii, E. M., 1976 Convective Stability of Incompressible Fluids (Translated from the Russian by D. Louvish). Jerusalem: Keter Publications.
Gershuni, G. Z. & Zhukhovitskii, E. M., 1982 Monotonic and oscillatory instabilities of a two-layer system of immiscible liquids heated from below. Sov. Phys. Dokl. 27, 531–533.Google Scholar
Hodgman, C. D. (ed.) 1960 Handbook of Chemistry and Physics, 42nd edn. Cleveland, Ohio: The Chemical Rubber Publishing Co.
Nguyen, A. T. & Kulacki, F. A., 1980 Convection in multi-layer systems. In Mechanisms of Continental Drift and Plate Tectonics (ed. P. A. Davis & S. K. Runcorn), pp. 259–266. Academic.
Pellew, A. & Southwell, R. V., 1940 On maintained convective motion in a fluid heated from below. Proc. R. Soc. Lond. A 176, 312–343.Google Scholar
Proctor, M. R. E. & Jones, C. A. 1988 The interaction of two spatially resonant patterns in thermal convection, I. Exact 1:2 resonance. J. Fluid. Mech. 188, 301–335.Google Scholar
Rasenat, S.: 1987 Konvektion in zwei geschichteten Flüssigkeiten. Diploma thesis, Institute of Physics, University of Bayreuth.
Renardy, Y. & Joseph, D. D., 1985 Oscillatory instability in a Bénard problem of two fluids. Phys. Fluids 28, 788–793.Google Scholar
Renardy, Y. & Renardy, M., 1985 Perturbation analysis of steady and oscillatory onset in a Bénard problem with two similar liquids. Phys. Fluids 28, 2699–2708.Google Scholar
Richter, F. M. & Johnson, G. E., 1974 Stability of a chemically layered mantle. J. Geophys. Res. 79, 1635–1639.Google Scholar
Schmeling, H.: 1988 Numerical models of Rayleigh-Taylor instabilities superimposed with convection. Preprint, Institute of Geology, Uppsala University.
Zeren, R. W. & Reynolds, W. C., 1972 Thermal instabilities in two-fluid horizontal layers. J. Fluid Mech. 53, 305–327.Google Scholar