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Three-dimensional absolute and convective instabilities at the onset of convection in a porous medium with inclined temperature gradient and vertical throughflow

Published online by Cambridge University Press:  25 November 2009

LEONID BREVDO
LEONID BREVDO*
Affiliation:
Institute of Fluid and Solid Mechanics, University of Strasbourg/CNRS, 2 rue Boussingault, F 67000 Strasbourg, France
*
†Email address for correspondence: [email protected]
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Abstract

By using the mathematical formalism of absolute and convective instabilities, we study in this work the nature of unstable three-dimensional localized disturbances at the onset of convection in a flow in a saturated homogeneous porous medium with inclined temperature gradient and vertical throughflow. It is shown that for marginally supercritical values of the vertical Rayleigh number Rv the destabilization has the character of absolute instability in all the cases in which the horizontal Rayleigh number Rh is zero or the Péclet number Qv is zero. In all the cases in which Rh and Qv are both different from zero, at the onset of convection the instability is convective. In the latter cases, the growing emerging disturbance has locally the structure of a non-oscillatory longitudinal roll, and its group velocity points in the direction opposite the direction of the applied horizontal temperature gradient, i.e. parallel to the axis of the roll. The speed of propagation of the unstable wavepacket increases with Qv and generally increases with Rh.

JFM classification

Low-Reynolds-number flows: Porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 641 , 25 December 2009 , pp. 475 - 487
Copyright
Copyright © Cambridge University Press 2009

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