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The effects of temperature-dependent viscosity and the instabilities in convection rolls of a layer of fluid-saturated porous medium

Published online by Cambridge University Press:  26 April 2006

A. C. Or
A. C. Or
Affiliation:
Division of Applied Sciences, Harvard University, Cambridge, MA 02138, USA Present address: Hughes Aircraft Company, S & CG, S41, B320, P. O. Box 92919, CA 90009, USA.
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Abstract

Convection of two-dimensional rolls in an infinite horizontal layer of fluid-saturated porous medium heated from below is studied numerically. Several important finite-amplitude states are isolated, and their bifurcation properties are shown. Effects of the temperature-dependent viscosity are included. The stability of these states is investigated with respect to the class of disturbances that have a ½π phase shift relative to the basic state. In particular, the oscillatory mechanism and the mean-flow generating mechanism through the variable viscosity are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 206 , September 1989 , pp. 497 - 515
Copyright
© 1989 Cambridge University Press

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References

Aidun, C. K. & Steen, P. H. 1987 Transition to oscillatory convective heat transfer in a fluid-saturated porous medium. J. Thermophys. 1, 268–273.Google Scholar
Busse, F. H. 1967 On the stability of two-dimensional convection in a layer heated from below. J. Maths & Phys. 46, 140–150.Google Scholar
Busse, F. H. 1983 Generation of mean flows by thermal convection. Physica 9D, 287–299.Google Scholar
Busse, F. H. & Clever, R. M. 1979 Instabilities of convection rolls in a fluid of moderate Prandtl number. J. Fluid Mech. 91, 319–335.Google Scholar
Busse, F. H. & Or, A. C. 1986 Subharmonic and asymmetric convection rolls. Z. Angew. Math. Phys. 37, 608–623.Google Scholar
Combarnous, M. & Le Fur, B. 1969 Transfert de chaleur par convection naturolle dans une couche poreuse horizontale. C. R. Acad. Sci. Paris 269B, 1009.Google Scholar
Foster, T. D. 1971 Intermittent convection. Geophys. Fluid Dyn. 2, 201–217.Google Scholar
Hager, B. H. & O'Connell, R. J. 1981 A simple global model of plate dynamics and mantle convection. J. Geophys. Res. 86, 4843–4867.Google Scholar
Horne, R. N. & O'Sullivan, M. J. 1974 Oscillatory convection in a porous medium heated from below. J. Fluid Mech. 66, 339–352.Google Scholar
Horne, R. N. & O'Sullivan, M. J. 1978 Origin of oscillatory convection in porous medium heated from below. Phys Fluids 21, 1260–1264.Google Scholar
Kimura, S., Schubert, G. & Straus, J. M. 1986 Route to chaos in porous medium thermal convection. J. Fluid Mech. 166, 305–324.Google Scholar
Krishnamurti, R. 1970 On the transition to turbulent convection. Part 2. The transition to time-dependent flow. J. Fluid Mech. 42, 309–320.Google Scholar
Moore, D. R. & Weiss, N. O. 1973 Two-dimensional Rayleigh-Bénard convection. J. Fluid Mech. 58, 289–312.Google Scholar
Or, A. C. & Busse, F. H. 1987 Convection in a rotating cylindrical annulus. Part 2. Transition to asymmetric and vascillating flow. J. Fluid Mech. 174, 313–326.Google Scholar
Saffman, P. G. & Taylor, G. I. 1958 The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid.. Proc. R. Soc. Lond. A 245, 312–329.Google Scholar
Schubert, G. & Straus, J. M. 1979 Three-dimensional and multicellular steady and unsteady convection in fluid-saturated porous media at high Rayleigh numbers. J. Fluid Mech. 94, 25–38.Google Scholar
Schubert, G. & Straus, J. M. 1982 Transitions in time-dependent thermal convection in fluid-saturated porous media. J. Fluid Mech. 121, 301–313.Google Scholar
Secel, L. A. 1962 The nonlinear interaction of two disturbances in the thermal convection problem. J. Fluid Mech. 14, 97–114.Google Scholar
Steen, P. H. & Aidun, C. K. 1988 Time-periodic convection in porous media: Transition mechanism. J. Fluid Mech. 196, 263–291.Google Scholar
Straus, J. M. 1974 Large amplitude convection in porous media. J. Fluid Mech. 64, 51.Google Scholar
Straus, J. M. & Schubert, G. 1979 Three-dimensional convection in a cubic box of fluid-saturated porous material. J. Fluid Mech. 91, 155–165.Google Scholar