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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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