High Rayleigh number convection in a three-dimensional porous medium

• Published in: Journal of fluid mechanics 2014-06, Vol.748, p.879-895
• Main Authors: Hewitt, Duncan R., Neufeld, Jerome A., Lister, John R.
• Format: Article
• Language: English
• Subjects: Buoyancy-driven instability; Convection; Exact sciences and technology; Flows through porous media; Fluid dynamics; Fluid mechanics; Fundamental areas of phenomenology (including applications); Geophysics; Hydrodynamic stability; Nonhomogeneous flows; Pattern selection; pattern formation; Physics; Porosity; Porous media; Rayleigh number
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2014.216

High-resolution numerical simulations of statistically steady convection in a three-dimensional porous medium are presented for Rayleigh numbers $Ra \leqslant 2 \times 10^4$ . Measurements of the Nusselt number $Nu$ in the range $1750 \leqslant Ra \leqslant 2 \times 10^4$ are well fitted by a relationship of the form $Nu = \alpha _3 Ra + \beta _3$ , for $\alpha _3 = 9.6 \times 10^{-3}$ and $\beta _3 = 4.6$ . This fit indicates that the classical linear scaling $Nu \sim Ra$ is attained, and that $Nu$ is asymptotically approximately $40\, \%$ larger than in two dimensions. The dynamical flow structure in the range $1750 \leqslant Ra \leqslant 2\times 10^4$ is analysed, and the interior of the flow is found to be increasingly well described as $Ra \to \infty $ by a heat-exchanger model, which describes steady interleaving columnar flow with horizontal wavenumber $k$ and a linear background temperature field. Measurements of the interior wavenumber are approximately fitted by $k\sim Ra^{0.52 \pm 0.05}$ , which is distinguishably stronger than the two-dimensional scaling of $k\sim Ra^{0.4}$ .