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High Rayleigh number convection in a porous medium containing a thin low-permeability layer

  • Duncan R. Hewitt (a1), Jerome A. Neufeld (a1) (a2) (a3) and John R. Lister (a1)
Abstract
Abstract

Porous geological formations are commonly interspersed with thin, roughly horizontal, low-permeability layers. Statistically steady convection at high Rayleigh number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Ra}$ is investigated numerically in a two-dimensional porous medium that is heated at the lower boundary and cooled at the upper, and contains a thin, horizontal, low-permeability interior layer. In the limit that both the dimensionless thickness $h$ and permeability $\Pi $ of the low-permeability layer are small, the flow is described solely by the impedance of the layer $\Omega = h/\Pi $ and by $\mathit{Ra}$ . In the limit $\Omega \to 0$ (i.e. $h \to 0$ ), the system reduces to a homogeneous Rayleigh–Darcy (porous Rayleigh–Bénard) cell. Two notable features are observed as $\Omega $ is increased: the dominant horizontal length scale of the flow increases; and the heat flux, as measured by the Nusselt number $\mathit{Nu}$ , can increase. For larger values of $\Omega $ , $\mathit{Nu}$ always decreases. The dependence of the flow on $\mathit{Ra}$ is explored, over the range $2500 \leqslant \mathit{Ra} \leqslant 2\times 10^4$ . Simple one-dimensional models are developed to describe some of the observed features of the relationship $\mathit{Nu}(\Omega )$ .

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Email address for correspondence: drh39@cam.ac.uk
References
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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