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Structure and mechanism of oscillatory convection in a cube of fluid-saturated porous material heated from below

  • Michael D. Graham (a1) and Paul H. Steen (a1)
Abstract

The transition from steady to oscillatory three-dimensional convection in a cube of saturated porous material is calculated to occur at Rayleigh number R = 584 due to seven pairs of thermal blobs which circulate around the cube. This travelling wave instability is shown to be closely related, first as regards structural characteristics and then as regards mechanism of instability, to an analogous instability in two dimensions. The correspondence with the two-dimensional flow is established via a correspondence with a nonlinear base flow in a box of square planform of a different aspect ratio (l/√2) and ultimately derives from the symmetries of the base flow in the cube.

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Aidun, C. K. & Steen, P. H. 1986 Transition to unsteady convective heat transfer in a fluid-saturated porous medium. AIAA/ASME 4th Joint Thermophysics and Heat Transfer Cerf., AIAA Paper 86–1264.
Aidun, C. K. & Steen, P. H. 1987 Transition to oscillatory convective heat transfer in a fluid-saturated porous medium. J. Thermophys. Heat Transfer 1, 268273.
Beck, J. L. 1972 Convection in a box of porous material saturated with fluid. Phys. Fluids 15, 13771383.
Caltagirone, J.-P. & Fabrie, P. 1989 Natural convection in a porous medium at high Rayleigh numbers Part I — Darcy's model. Eur. J. Mech. B 8, 207227.
Caltagirone, J.-P., Fabrie, P. & Combarnous, M. 1987 De la convection naturelle oscillante en milieu poreux an chaos temporel? C. R. Acad. Sci. Paris 305 (II), 549553.
Cubby, J. H., Herring, J. R., Loncaric, J. & Orszag, S. A. 1984 Order and disorder in two- and three-dimensional Bénard convection. J. Fluid Mech. 147, 138.
DOedel, E. J. 1981 AUTO: a program for the automatic bifurcation analysis of autonomous systems. Congressus Numerantum 30, 265284. (Also Proc. 10th Manitoba Conf. on Numerical Mathematics and Computation, University of Manitoba, Winnepeg, Canada, 1980).
Fabrie, P. 1986 Solutions fortes et comportement asymptotique pour un modèle de convection naturelle en milieu poreux. Acta Applicandae Mathematicae 7, 4977.
Gollub, J. P. & Benson, S. V. 1980 Many routes to turbulent convection. J. Fluid Mech. 100, 447470.
Golubitsky, M. G. & Schaeffer, D. G. 1985 Singularities and Groups in Bifurcation Theory, vol. 1. Springer.
Graham, M. D. & Steen, P. H. 1991 Strongly interacting traveling waves and quasiperiodic dynamics in porous medium convection. Physica D (submitted).
Horne, R. N. 1979 Three-dimensional natural convection in a confined porous medium heated from below. J. Fluid Mech. 92, 751766.
Kimura, S., Schubert, G. & Steaus, J. M. 1986 Route to chaos in porous-medium thermal convection. J. Fluid Mech. 207, 153189.
Kimura, S., Schubert, G. & Straus, J. M. 1989 Time-dependent convection in a fluid-saturated porous cube heated from below. J. Fluid Mech. 207, 153189 (referred to herein as KSS).
Lennie, T. B., McKenzie, D. P., Moore, D. R. & Weiss, N. O. 1988 The breakdown of steady convection. J. Fluid Mech. 188, 4785.
McLaughlin, J. B. & Orszag, S. A. 1982 Transition from periodic to chaotic thermal convection. J. Fluid Mech. 122, 123142.
Stamps, D. W., Arpaci, V. S. & Clark, J. A. 1990 Unsteady three-dimensional natural convection in a fluid saturated porous medium. J. Fluid Mech. 213, 377396.
Steen, P. H. 1983 Pattern selection for finite-amplitude convection states in a box of porous media. J. Fluid Mech. 136, 219241.
Steen, P. H. 1986 Container geometry and the transition to unsteady Bénard convection in porous media. Phys. Fluids 29, 925933.
Steen, P. H. & Aidun, C. K. 1988 Time-periodic convection in porous media: transition mechanism. J. Fluid Mech. 196, 263290.
Titi, E. S. 1991 Gevrey class regularity and long time approximations for 3-D convection in porous media (in preparation).
Veronis, G. 1965 Large-amplitude Bénard convection. J. Fluid Mech. 26, 4968.
Zebib, A. & Kassoy, D. R. 1978 Three-dimensional natural convection motion in a confined porous medium. Phys. Fluids 21, 13.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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