Instabilities of Steady, Periodic, and Quasi-Periodic Modes of Convection in Porous Media

[+] Author and Article Information
S. Kimura, G. Schubert

Department of Earth and Space Sciences, University of California, Los Angeles, CA 90024

J. M. Straus

Space Sciences Laboratory, The Aerospace Corporation, Los Angeles, CA 90009

J. Heat Transfer 109(2), 350-355 (May 01, 1987) (6 pages) doi:10.1115/1.3248087 History: Received February 14, 1986; Online October 20, 2009


Instabilities of steady and time-dependent thermal convection in a fluid-saturated porous medium heated from below have been studied using linear perturbation theory. The stability of steady-state solutions of the governing equations (obtained numerically) has been analyzed by evaluating the eigenvalues of the linearized system of equations describing the temporal behavior of infinitesimal perturbations. Using this procedure, we have found that time-dependent convection in a square cell sets in at Rayleigh number Ra=390. The temporal frequency of the simply periodic (P(1) ) convection at Rayleigh numbers exceeding this value is given by the imaginary part of the complex eigenvalue. The stability of this (P(1) ) state has also been studied; transition to quasi-periodic convection (QP2 ) occurs at Ra ≈ 510. A reverse transition to a simply periodic state (P(2) ) occurs at Ra ≈ 560; a slight jump in the frequency of the P(2) state occurs at Ra between 625 and 640. The jump coincides with a second narrow (in terms of Ra) region of quasi-periodicity.

Copyright © 1987 by ASME
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