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On Hadley flow in a porous layer with vertical heterogeneity

Published online by Cambridge University Press:  29 August 2012

A. Barletta  and
D. A. Nield
A. Barletta*
Affiliation:
DIENCA, Alma Mater Studiorum – Università di Bologna, Viale Risorgimento 2, I-40136 Bologna, Italy
D. A. Nield
Affiliation:
Department of Engineering Science, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
*
†Email address for correspondence: [email protected]
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Abstract

The onset of thermoconvective instability in a horizontal porous layer with a basic Hadley flow is studied, under the assumption of weak vertical heterogeneity. Hadley flow is a single-cell convective circulation induced by horizontal linear changes of the layer boundary temperatures. When combined with heating from below, these thermal boundary conditions yield a temperature gradient inclined to the vertical, in the basic state. The linear stability of the basic state is studied by considering small-amplitude disturbances of the velocity field and the temperature field. The linearized governing equations for the disturbances are then solved both by Galerkin’s method of weighted residuals and by a combined use of the Runge–Kutta method and the shooting method. The effect of weak heterogeneity of the permeability and the effective thermal conductivity of the porous medium is studied with respect to neutral stability conditions. It is shown that, among the normal mode disturbances, the most unstable are longitudinal rolls, that is, plane waves with a wave vector perpendicular to the imposed horizontal temperature gradient. The effect of heterogeneity becomes important only for high values of the horizontal Rayleigh number, associated with the horizontal temperature gradient, approximately greater than 60. In this regime, the effect of heterogeneity is destabilizing. It is shown that heterogeneity with respect to thermal conductivity is of major importance in the onset of instability.

JFM classification

Convection: Buoyancy-driven instability Convection: Convection in porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 710 , 10 November 2012 , pp. 304 - 323
Copyright
Copyright © Cambridge University Press 2012

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