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Transitions in time-dependent thermal convection in fluid-saturated porous media

Published online by Cambridge University Press:  20 April 2006

G. Schubert  and
J. M. Straus
G. Schubert
Affiliation:
Space Sciences Laboratory, The Aerospace Corporation, P.O. Box 92957, Los Angeles, CA 90009
J. M. Straus
Affiliation:
Space Sciences Laboratory, The Aerospace Corporation, P.O. Box 92957, Los Angeles, CA 90009
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Abstract

Numerical simulations of single-cell, two-dimensional, time-dependent thermal convection in a square cross-section of fluid-saturated porous material heated uniformly from below reveal a series of transitions between distinct oscillatory dynamical regimes. With increasing Rayleigh number R, the flow first evolves from steady-state behaviour into periodic motion with a single frequency f which depends on R approximately according to $f\propto R^{\frac{7}{8}}$ the transition Rayleigh number lies between about 380 and 400. At a value of R between about 480 and 500 the flow transforms into a fluctuating state characterized by two frequencies. Soon thereafter, for R between about 500 and 520, it reverts back to single-frequency periodic behaviour with f approximately proportional to $R^{\frac{3}{2}}$. The two frequencies in the narrow transition regime may be locked to a rational ratio, in which case the flow is periodic, or they may be commensurate, in which case the flow is quasi-periodic. The spectral characteristics of numerical realizations of unsteady convection and the occurrences of transitions therein are highly dependent on truncation level in Galerkin schemes or resolution in finite-difference approaches.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 121 , August 1982 , pp. 301 - 313
Copyright
© 1982 Cambridge University Press

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References

Caltagirone, J. P. 1974 Convection naturelle fluctuante en milieu poreux. C. R. Acad. Sci. Paris 278 B, 259.Google Scholar
Caltagirone, J. P. 1975 Thermoconvective instabilities in a horizontal porous layer. J. Fluid Mech. 72, 169.Google Scholar
Caltagirone, J. P., Cloupeau, M. & Combarnous, M. 1971 Convection naturelle fluctuante dans une couche poreuse horizontale. C. R. Acad. Sci. Paris 273 B, 833.Google Scholar
Combarnous, M. & Lefur, B. 1969 Transfer de chaleur par convection naturelle dans une couche poreuse horizontale. C. R. Acad. Sci. Paris 269 B, 1009.Google Scholar
Fenstermacher, P. R., Swinney, H. L. & Gollub, J. P. 1979 Dynamical instabilities and the transition to chaotic Taylor vortex flow. J. Fluid Mech. 94, 103.Google Scholar
Gollub, J. P. & Benson, S. V. 1980 Many routes to turbulent convection. J. Fluid Mech. 100, 449.Google Scholar
Horne, R. N. & O'Sullivan, M. J.1974 Oscillatory convection in a porous medium heated from below. J. Fluid Mech. 66, 339.Google Scholar
Horne, R. N. & O'Sullivan, M. J.1978 Origin of oscillatory convection in a porous medium heated from below. Phys. Fluids 21, 1260.Google Scholar
Horton, C. W. & Rogers, F. T. 1945 Convection currents in a porous medium. J. Appl. Phys. 16, 367.Google Scholar
Lapwood, E. R. 1948 Convection of a fluid in a porous medium. Proc. Camb. Phil. Soc. 44, 508.Google Scholar
Marcus, P. S. 1981 Effects of truncation in modal representations of thermal convection. J. Fluid Mech. 103, 241.Google Scholar
Mclaughlin, J. B. & Orszag, S. A. 1982 Transition from periodic to chaotic thermal convection. J. Fluid Mech. (in the press).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.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 fluidsaturated porous material. J. Fluid Mech. 91, 155.Google Scholar
Straus, J. M. & Schubert, G. 1981 Modes of finite-amplitude three-dimensional convection in rectangular boxes of fluid-saturated porous material. J. Fluid Mech. 103, 23.Google Scholar
Toomre, J., Gough, D. O. & Spiegel, E. A. 1977 Numerical solutions of single-mode convection equations. J. Fluid Mech. 79, 1.Google Scholar